Problemas e Soluciones de Calculus
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Questions and Answers

Calcula le integral: √(2x + 1)²⁰ dx

1/21 * (2x + 1)²¹ + C

Calcula le integral: dx / (x² + a²)

1/a * arctg( x/a ) + C

Calcula le integral: dx / √(a² - x²)

arcsin( x/a ) + C

Calcula le integral: √(a² - x²) dx

<p>a * arcsin (x/a) + C</p> Signup and view all the answers

Calcula le integral: tgx dx

<p>ln|secx| + C</p> Signup and view all the answers

Calcula le integral: dx / (x-1)^4

<p>1/3*(x-1)^-3 + C</p> Signup and view all the answers

Calcula le integral: sinx d(sinx)

<p>(sin²x)/2 + C</p> Signup and view all the answers

Calcula le integral: (x + 1)^15 dx

<p>1/16 (x + 1)^16 + C</p> Signup and view all the answers

Calcula le integral: cos3x d(3x)

<p>sin3x + C</p> Signup and view all the answers

Calcula le integral: cos(1 - 2x) dx

<p>-1/2 * sin(1 - 2x) + C</p> Signup and view all the answers

Calcula le integral: ax^(3x) dx

<p>(a/3ln(a)) * a^(3x) + C</p> Signup and view all the answers

Calcula le integral: dx / √(1 - 25x²)

<p>1/5 * arcsin(5x) + C</p> Signup and view all the answers

Study Notes

Calculus Problems and Solutions

  • Indefinite Integrals: Numerous problems involving finding indefinite integrals with various functions, including polynomials, trigonometric functions, and inverse trigonometric functions. Solutions provided in the form of expressions, plus an integration constant 'c'.

  • Definite Integrals: Problems focus on calculating definite integrals, often covering basic functions and techniques. Solutions provide numerical results.

  • Trigonometric Integrals: Specific examples of integrating trigonometric functions (e.g., sin x, cos x, tan x). Various problem types shown, including simple and composite trigonometric functions.

  • Inverse Trigonometric Integrals: Problems involving integration of inverse trigonometric functions (e.g., arcsin, arccos, arctan). Detailed solutions presented for these examples.

  • Integration by Substitution: Problems demonstrate the application of the integration by substitution method for various functions, providing step-by-step solutions.

  • Integration by Parts: Problems show how the method of integration by parts is used to solve integrals. Demonstrates step-by-step solutions to complicated problems.

  • Other Integration Techniques: Problems are presented using various other integration methods such as simplification, factorization, and trigonometric identities. Detailed solutions are provided.

  • Problems with Variables: Examples integrate expressions including variables, offering a comprehensive review of different integrand functions. Solutions provide calculated results for these.

  • Series and sequences: Problems in determining convergence and divergence of infinite series and sequences, with relevant mathematical tests and theorems. Includes several examples of finding convergence intervals.

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Description

Este quiz explora diversas problemáticas de integrales, incluindo integrales indefinidas e definidas, juntamente com funções trigonométricas e funciones trigonométricas inversas. Soluciones detalladas são oferecidas, ajudando na compreensão da integração por substituição. Prepare-se para testar seu conhecimento em cálculo!

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