Chapter 14.1, Problem 10E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating an Integral In Exercises 3-10, evaluate the integral. ∫ y π □ 2 sin 3 x cos y   d x

To determine

To calculate: The value of integral yπ2sin3xcosydx.

Explanation

Given:

The integral is âˆ«yÏ€2sin3xcosydx.

Formula used:

Use the basic formulas of integration:

âˆ«sinxâ€‰dx=âˆ’cosx+Csin2x=1âˆ’cos2xâˆ«xndx=xn+1n+1+C

Where; C is integration constant.

Calculation:

Here, the integration is performed with respect to y, so the variable x is treated to be constant.

Now, use the method of substitution as:

Substitute, cosx=u

Differentiate both sides and get, âˆ’sinxâ€‰dx=du.

When x=y, then

u=cosx=cosy

When x=Ï€2, then,

u=cosx=cosÏ€2=0

Now,

âˆ«yÏ€2sin3xcosydx=cosyâˆ«yÏ€2sin<

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