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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.

2 2 ( x 4 + 2 x 2 5 ) d x

To determine

To calculate: The definite integral 22(x4+2x25)dx.

Explanation

Given Information:

The provided definite integral is 22(x4+2x25)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 power rule of integrals:

undu=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:

22(x4+2x25)dx

Now apply, the property of definite integrations:

22(x4+2x25)dx=22(x4)dx+222(x2)dx522(x0)dx

Now apply, the power rule of integration:

22(x4)dx+2∫<

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