RD-Sharma-Class-12-Maths-Solutions-Chapter-19-Indefinite-Integrals.pdf

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.1 Page No: 19.4 1. Evaluate the following integrals: Solution: Given Solution: Given ...

RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.1 Page No: 19.4 1. Evaluate the following integrals: Solution: Given Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given 2. Evaluate: Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given 3. Evaluate: Solution: Given RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.2 Page No: 19.14 Evaluate the following integrals (1 - 44): Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Given RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.3 Page No: 19.23 Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.4 Page No: 19.30 Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.5 Page No: 19.33 Solution: Given  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.6 Page No: 19.36 Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.7 Page No: 19.38 Integrate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.8 Page No: 19.47 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.9 Page No: 19.57 Evaluate the following integrals: dx Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.10 Page No: 19.65 Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.11 Page No: 19.69 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.12 Page No: 19.73 Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.13 Page No: 19.79 Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.14 Page No: 19.83 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.15 Page No: 19.86 Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.16 Page No: 19.90 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.17 Page No: 19.93 Evaluate the following integrals: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.18 Page No: 19.98 Evaluate the following integrals: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: Solution: Let sin x = t  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.19 Page No: 19.104 Evaluate the following integrals: Solution: We will solve I1 and I2 individually. RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.20 Page No: 19.106 Evaluate the following integrals: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: ⇒ 1 = (A + B) x + (3A – 2B) ⇒ Then A + B = 0 … (1) And 3A – 2B = 1 … (2) Solving (1) and (2), 2 × (1) → 2A + 2B = 0 1 × (2) → 3A – 2B = 1 5A = 1 ∴ A = 1/5  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Substituting A value in (1),  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.21 Page No: 19.110 Evaluate the following integrals: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.22 Page No: 19.114 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.23 Page No: 19.117 Evaluate the following integrals: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.24 Page No: 19.122 Evaluate the following integrals: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.25 Page No: 19.133 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.26 Page No: 19.143 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.27 Page No: 19.149 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.28 Page No: 19.154 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.29 Page No: 19.158 Evaluate the following integrals: Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.30 Page No: 19.176 Evaluate the following integrals: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.31 Page No: 19.190 Evaluate the following integrals: Solution: The given equation can be written as,  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Exercise 19.32 Page No: 19.196 Evaluate the following integrals: Solution: Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution:  RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Solution: RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals