   Chapter 4, Problem 39RE

Chapter
Section
Textbook Problem

Using Properties of Definite Integrals Given ∫ 4 8 f ( x )   d x = 12 and ∫ 4 8 g ( x )   d x = 5 , evaluate(a) ∫ 4 8 [ f ( x ) − g ( x ) ] = d x (b) ∫ 4 8 [ f ( x ) − g ( x ) ] d x (c) ∫ 4 8 [ 2 f ( x ) − 3 g ( x ) ] d x (d) ∫ 2 5 − 8 f ( x ) d x

(a)

To determine

To calculate: The value of I=48[ f(x)g(x) ]dx using given integrals 48f(x)dx=12,48g(x)dx=5.

Explanation

Given:

The integral is 48f(x)dx=12,48g(x)dx=5.

Formula used:

ab[ f(x)g(x) ]dx=abf(x)dxabg(x)dx

Calculation:

Consider the given integral

(b)

To determine

To Calculate: The value of I=48[ 2f(x)3g(x) ]dx using given integrals 48f(x)dx=12,48g(x)dx=5.

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