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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5, Problem 62RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

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+2x2−5)dx.

Explanation

Given Information:

The provided definite integral is ∫−22(x4+2x2−5)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+2x2−5)dx

Now apply, the property of definite integrations:

∫−22(x4+2x2−5)dx=∫−22(x4)dx+2∫−22(x2)dx−5∫−22(x0)dx

Now apply, the power rule of integration:

∫−22(x4)dx+2∫<

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