   Chapter 4.4, Problem 38E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 1 ( 1 + x 2 ) 3 d x

To determine

To evaluate:

011+x23 dx

Explanation

1) Concept:

By using the fundamental theorem of calculus and the rules of integration, evaluate the given integral.

The fundamental theorem of calculus:

If f is continuous on [a, b], then abfxdx=Fb-F(a).

2) Formula:

fx+gxdx=fxdx+gxdx

xndx=xn+1n+1+C

kdx=kx+C

3) Given:

011+x23 dx

4) Calculation:

Consider, 011+x23 dx

By using the polynomial expansion,

011+x23 dx= 01(1+3x2+3x4+x6)  dx

After separating the integrals,

01(1+3x2+3x4+x6)  dx=011dx+013x2dx+013x4dx+01x6d

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