   Chapter 4.3, Problem 19E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 1 3 ( x 2 + 2 x − 4 ) d x

To determine

To evaluate: 13(x2+2x-4)dx

Explanation

1) Concept:

i) The Fundamental Theorem of Calculus (part 2)

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

2) Theorem:

The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then

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

3) Calculation: 13(x2+2x-4)dx

By separating the integration

13x2dx+132xdx-134dx

By using the antiderivative of each term,

13x2dx+132xdx-13

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