   Chapter 13.6, Problem 6E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-16, use integration by parts to evaluate the integral. ∫ 0 1 y ( 1 − y ) 3 / 2 d y

To determine

To calculate: The value of the integral 01y(1y)3/2dy with the help of integral by parts.

Explanation

Given Information:

The provided integral is 01y(1y)3/2dy.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

For any variable u, the integral formula is,

undu=un+1n+1+C

Calculation:

Consider the provided integral:

01y(1y)3/2dy

Now, split the integrand into two parts setting one part equal to u and another part equal to dv.

So, the values will be:

u=y

And,

dv=(1y)3/2dy

Then, differentiate u=y on both sides with respect to u,

du=(1)dy

Also, integrate the equation dv=(1y)3/2dy by the use of formula undu=un+1n+1+C.

v=(1y)3/2dy=25(1y)5/2

Then, use the formula for integration by parts:

udv=uv

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