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Chapter 5: Q 11. (page 451)

Describe strategy for solving the type of integral given.
$\int c o t^{k} x d x, k$ even.

Short Answer

Expert verified

Write $c o t x = u$

Step by step solution

Step 1. Given information

Integral is $\int c o t^{k} x d x$

Step 2. Explanation

Consider the integral $\int c o t^{k} x d x, k$ even

Let $c o t x = u$ and use the formula $(c o t x)' = - c s c^{2} x$

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Most popular questions from this chapter

Find three integrals in Exercises 27–70 for which a good strategy is to apply integration by parts twice.

Suppose $u (x) = x^{2}$ . Calculate and compare the values of the following definite integrals:

role="math" localid="1648786835678" $\int_{- 1}^{5} u^{2} d u, \int_{x = - 1}^{x = 5} u^{2} d u and \int_{u (- 1)}^{u (5)} u^{2} d u$

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Explain why, if $x = a \tan u$ , then $\sqrt{x^{2} + a^{2}} = a s e c u$ . Your explanation should include a discussion of domains and absolute values.

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Describe strategy for solving the type of integral given.
$\int c o t^{k} x d x, k$ even.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Describe strategy for solving the type of integral given.∫cotkxdx,keven.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Decision Maths

Calculus

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Describe strategy for solving the type of integral given.
$\int c o t^{k} x d x, k$ even.