   Chapter 13.6, Problem 5E ### 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. ∫ 4 4 q q − 4   d q

To determine

To calculate: The value of the integral 46qq4dq with the help of integral by parts.

Explanation

Given Information:

The provided integral is 46qq4dq.

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:

46qq4dq

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=q

And,

dv=(q4)1/2dq

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

du=1dq

Also, integrate the equation dv=(q4)1/2dq by the use of formula undu=un+1n+1+C.

v=(q4)1/2dq=23(q4)3/2

Now, use the formula for integration by parts:

udv=uvvdu

And evaluate further, by the use of formula

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