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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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Evaluating a Definite Integral In Exercises 59–70, evaluate the definite integral.

3 6 x 3 x 2 8 d x

To determine

To calculate: The definite integral 36(x3x28)dx.

Explanation

Given Information:

The provided definite integral is 36(x3x28)dx.

Formula used:

The sum and difference property of definite integrations:

ab[f(x)±g(x)]dx=ab[f(x)]dx±ab[g(x)]dx

The general power rule of integrals:

undudxdx=un+1n+1+C

The fundamental theorem of calculus:

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

Here, F is function such that F(x)=f(x) for all x in [a,b].

Calculation:

Consider the indefinite integral:

36(x3x28)dx

The property of definite integrations:

36(x3x28)dx=13(12)36(x2

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