   Chapter 4.4, Problem 36E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 64 u ( u − u 3 ) d u

To determine

To evaluate:

064uu-u3du

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) where F is the anti derivative of f.

2) Formula:

fx+gxdx=fxdx+gxdx

xndx=xn+1n+1+C

kdx=kx+C

3) Given:

064uu-u3du

4) Calculation:

Consider, 064uu-u3du

By using the rules of exponent,

064uu-u3du= 064u12u-u13du= 064u32-u56du

After separating the integrals,

064u32-u56du=0<

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