   Chapter 5.2, Problem 22E ### 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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# Applying the General Power Rule In Exercises 9-34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5. ∫ t 4 t 5   −   9 3   d t

To determine

To calculate: The value of the provided indefinite integral t4t593dt.

Explanation

Given Information:

The provided indefinite integral is t4t593dt.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C,

Where n1

Calculation:

Consider the indefinite integral say I,

I=t4t593dt

Above integral can be written in rational exponent form as;

I=t4(t59)13dt

Multiply and divide by 5 in the right-hand side of above integral;

I=15(5t4)(t59)13dt

Take the factor 15 out of the integrand;

I=15(5t4)(t59)13dt

Let

t59=u … (1)

Differentiate the above equation with respect to t;

ddt(t59)=dudtddt(t5)ddt(9)=dudt5t4=dudt</

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