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Chapter 5: Q 10. (page 451)

Describe strategies for solving the types of integrals given.
$\int co t^{k} x d x, k$ odd

Short Answer

Expert verified

Take $c o t x = u$

Step by step solution

Step 1. Given information

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

Step 2. Explanation

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

Take $c o t x = u$

Also, use the formula: $(c o t x)' = - c s c^{2} x$

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Most popular questions from this chapter

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution with $x = a \sin u$ or $x = a \tan u$ ? Why do we need to think about the unit circle after trigonometric substitution with $x = a s e c u$ ?

Consider the integral $\int \sin x \cos x d x$ .

(a) Solve this integral by using u-substitution with $u = \sin x$ and $d u = \cos x d x$ .

(b) Solve the integral another way, using u-substitution with $u = \cos x$ and $d u = - \sin x d x$ .

Explain why using trigonometric substitution with $x = a \tan u$ often involves a triangle with side lengths a and x and hypotenuse of length $\sqrt{x^{2} + a^{2}}$

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.

$u (x) = x^{2} + 1$

Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

$2 x^{2} - 4 x + 1$

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Describe strategies for solving the types of integrals given.
$\int co t^{k} x d x, k$ odd

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Most popular questions from this chapter

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Describe strategies for solving the types of integrals given.∫cotkxdx,kodd

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

Calculus

Geometry

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Describe strategies for solving the types of integrals given.
$\int co t^{k} x d x, k$ odd