   Chapter 4.2, Problem 43E

Chapter
Section
Textbook Problem

# In Example 4.1.2 we showed that ∫ 0 1 x 2   d x = 1 3 . Use this fact and the properties of integrals to evaluate ∫ 0 1 ( 5 − 6 x 2 ) d x

To determine

To evaluate:

The integral 01(5-6x2)dx

Explanation

1) Concept:

i. ab[fx+gx] dx=abfxdx+abgxdx

ii. abcfxdx=cabfxdx

iii.

abx2 dx=b3-a33

2) Given:

01x2dx=13

3) Calculation:

By using the property (i), the integral becomes

01x2dx=015dx-  0

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