   Chapter 4.3, Problem 22E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 1 ( 1 − 8 v 3 + 16 v 7 ) d v

To determine

To evaluate: 01(1-8v3+16v7)dv

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:

01(1-8v3+16v7)dv By separating the integral

01(1-8v3+16v7)dv=011dv-018v

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