   Chapter 8.5, Problem 44E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating a Definite Integral In Exercises 39-46, evaluate the definite integral. See Example 6. ∫ π / 4 π / 2 cot 3   x   csc 2   x   d x

To determine

To calculate: The value of definite integral π/4π/2cot3xcsc2xdx.

Explanation

Given Information:

The provided integral is π/4π/2cot3xcsc2xdx.

Formula used:

Write the formula of definite integral of abundu.

abundu=[un+1n+1]ab

Here, n is the any positive integer.

Write the formula for derivative of cotu.

ddx[cotu]=csc2ududx

Calculation:

The provided integral is,

π/4π/2cot3xcsc2xdx

Rewrite.

π/4π/2cot3xcsc2xdx=π/4π/2cot3x(csc2xdx)

Let u=cotx.

Differentiate with the help of derivative of cotu.

du=csc2xdx

Substitute u for cotx and du for csc2xdx.

π/4π/2cot3xcsc2xdx=π/4π/2u3du

Integrate with the help of above integration formula

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