   Chapter 4.3, Problem 44E

Chapter
Section
Textbook Problem

Using Properties of Definite Integrals Given ∫ − 1 1 f ( x ) d x = 0     and   ∫ 0 1 f ( x ) d x = 5 evaluate ∫ − 1 0 f ( x ) d x ∫ 0 1 f ( x ) d x − ∫ − 1 0 f ( x )   d x ∫ − 1 1 3 f ( x ) d x ∫ 0 1 3 f ( x ) d x

(a)

To determine

To calculate: The definite integral 10f(x)dx using the provided values.

Explanation

Given:

The provided values are

11f(x)dx=0 and 01f(x)dx=5

And the integral to be evaluated is

10f(x)dx

Formula used:

The additive interval property is:

If f(x) is integrable on the three closed intervals determined by a,b and c, then

abf(x)dx=acf(x)dx+cbf(x)dx

Calculation:

We will start with the provided integral. we get,

11f(x)dx=0

As f(x) is integrable on the three closed intervals determined by a,b and c, then

abf

(b)

To determine

To calculate: The definite integral 01f(x)dx10f(x)dx using the provided values.

(c)

To determine

To calculate: The definite integral 113f(x)dx using the provided values.

(d)

To determine

To calculate: The definite integral 013f(x)dx using the provided values.

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