   Chapter 4.R, Problem 16E

Chapter
Section
Textbook Problem

# Evaluate the integral, if it exists. ∫ 0 1 ( u 4 + 1 ) 2 d u

To determine

To evaluate:

01u4+12du if it exists

Explanation

1) Concept:

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

2) Theorem:

Fundamental theorem of calculus:

If f is continuous on a, b, then abfxdx=Fb-Fa.

3) Formula:

xndx=xn+1n+1+C

3) Given:

01u4+12du

4) Calculation:

Consider, 01u4+12du

=01u14+12du

=01(u12+2u14+1) du

Since the function is continuous in the given interval, the integral exists

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