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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Area by the Fundamental Theorem In Exercises 9-16, find the area of the region. See Example 2.

y = x 2 x

Chapter 5.4, Problem 16E, Finding Area by the Fundamental Theorem In Exercises 9-16, find the area of the region. See Example

To determine

To calculate: The area of the region y=x2x in the provided figure.

Calculus: An Applied Approach (MindTap Course List), Chapter 5.4, Problem 16E

Explanation

Given Information:

The function is y=x2x and the provided figure is:

Formula used:

The fundamental theorem of calculus states that,

If f is integrable on interval [a,b] then abf(x)dx=F(b)F(a).

The integration formulas are,

xndx=xn+1n+1+C and 1xdx=lnx+C, where C is the constant.

Calculation:

Consider the given figure.

To find the area of the region, fundamental theorem of calculus can be used.

Integrate the function from 2 to 4 as shown below,

24(x2x)dx

This can be written as,

24(

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