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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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Definite Integral Involving Absolute Value In Exercises 39-42, evaluate the definite integral. See Example 5.

Definite Integral Involving Absolute Value In Exercises 39-42, evaluate the definite integral. See Example 5.

2 8 | 3 x 9 |   d x

To determine

To calculate: The value of integral 28|3x9|dx.

Explanation

Given Information:

The integral is 28|3x9|dx.

Formula used:

The integration sum rule for two function f and g continuous on close interval [a,b] is,

ab[f(x)±g(x)]dx=abf(x)dx±abg(x)dx

The fundamental theorem of calculus states that,

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

The integration formula is xndx=xn+1n+1+C.

The mathematical definition of absolute value is,

|x|={x, x<0  x, x0}

Calculation:

Consider the integral,

28|3x9|dx

The region represented by definite integral is shown on the given figure,

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