   Chapter 4.3, Problem 27E

Chapter
Section
Textbook Problem

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

To determine

To evaluate:

01u+2u-3 du

Explanation

1) Concept:

i) The Fundamental Theorem of Calculus (part 2): Suppose  f is continuous on [a, b], then

abfxdx=Fb-F(a), where F is antiderivative of  f, that is F'=f.

ii) Separate out the integration and then use antiderivative of each term

2) Calculation:

01u+2u-3 du

After simplifying the equation, the above integration becomes

01(u2-3u+2u-6) du= 01u2-u-6 du

After separating the integration, the above integration becomes

01u2 du-01

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