   Chapter 12.2, Problem 4E ### 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 each of Problems 5 and 6, one of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate the part that can be done with the Power Rule, and explain why the Power Rule cannot be used to evaluate the other.(a) ∫ 5 ( 6 + 5 x ) 10 d x (b) ∫ 14 x 2 ( 2 x 7 + 9 ) 6 d x

(a)

To determine

To calculate: The value of the integral 5(6+5x)10dx.

Explanation

Given Information:

The provided integral is 5(6+5x)10dx

Formula used:

According to the power formula of integrals, if u=u(x), then:

undu=un+1n+1+C

Calculation:

Consider the provided integral:

5(6+5x)10dx

Consider the power rule of integrals:

undu=un+1n+1+C

Now, to use the power rule, the integrand should have the function u(x) and its derivative u(x) and n1.

Here,

u=6+5x

Then, on obtaining differentials,

du=5

Thus,

u=6+5xn=10u=5

All required parts are present, so the integral is of the form,

5(6+5x)10dx=u10

(b)

To determine

To calculate: The value of the integral 14x2(2x7+9)6dx.

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