   Chapter 13, Problem 12RE ### 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

# Evaluate the integrals in Problems 7-18. ∫ 2 3 x 2 2 x 3 − 7 d x

To determine

To calculate: The value of the integral 23x22x37dx.

Explanation

Given Information:

The provided integral is,

23x22x37dx

Formula used:

Let f be a continuous function on the closed interval [a,b], then the definite integral of f exists on this interval and,

abf(x)dx=F(b)F(a)

According to the logarithmic rule of integrals,

1xdx=ln|x|+C

Calculation:

Consider the provided integral,

23x22x37dx

Now, rewrite the integral by dividing and multiplying by 6 as,

16236x22x37dx

Now, let 2x37=t, then on obtaining differentials,

6x2dx=dt

Thus, the integral becomes,

16236x22x37dx=1623dtt

Now, use the logarithmic rule of integrals to obtain the value o

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