Important PYQs on Indefinite Integration - Practice Quiz

Calculus and Trigonometry

• The value of g(-1) is not provided in the given expression.
• I(0) = 1 and I(π/3) = 3, therefore, the value of I(π/6) can be found using trigonometric identities.
• The integral ∫sin(x)sin(3x) + cos^2(x)dx evaluates to a specific value.
• If f(x) = ∫9.x [xf(x)(1 + x)^2 dx], then the value of f(0) is 0.
• The value of d^2I/dx^2 at x = 3 is related to the given function I(x) and its derivatives.
• The integral ∫(sec(x) * tan(x))dx is related to the given integral ∫(sec(x) * cot^3(x))dx.
• The value of the integral $∫4(2x - 1) + tan^{-1}(x + 1/x) dx$ is dependent on the constant of integration C.
• The expression $10(α + βγ + δ)$ evaluates to a specific value when given a certain integral.
• The integral of $\left(\frac{sin^n(θ) - sin(θ)}{sin^{n+1}(θ)cos(θ)}\right)dθ$ is related to natural numbers n ≥ 2 and 0 < θ < π/2.
• The function g:(0, ∞) → R satisfies the integral $∫(n - 1)sin^{n+1}(x)g(x)dx = 2 + C$.

Trigonometry

• If ∫ ( \frac{x}{1+x} )dx is equal to 2x + C, then the function f(x) is related to the integral.
• The value of f(4) is dependent on the value of f(3) and logarithmic identities.
• The value of ∫ sinθ⋅sin2θ(dx) is related to the expression: sin6θ + sin4θ, 1−cos2θ, θ + 9sin4θ − 2sin6θ.

Exponential Functions

• The function g(x) satisfies the integral ∫ ( e^{x+7} )dx = g(x)+C and g(1) = 0.

Algebraic Expressions

• The function A(x)tan⁻¹(√x)+B(x)+C is equivalent to the integral ∫ (x+1)/(√x)dx.
• The value of A in the integral ∫ [11 - 18sin²θ/(9sin⁴θ - 2sin⁶θ)]dθ = Alogₑ(x)+C is dependent on the given expression.