   Chapter 5.4, Problem 7E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Using Properties of Definite Integrals In Exercises 7 and 8, use the values                     ∫ 0 5 f(x) dx = 6 and                     ∫ 0 5 g ( x )   d x =   2 to evaluate each definite integral.                     ∫ 0 5 [ f ( x ) + g ( x ) ] d x     ( b ) ∫ 0 5 [ ( f ( x ) − g ( x ) ] d x (c)                     ∫ 0 5 − 4 f ( x ) d x     ( d ) ∫ 0 5 [ ( f ( x ) − 3 g ( x ) ] d x

(a)

To determine

To calculate: The definite integral of function 05[f(x)+g(x)]dx by using the values 05f(x)dx=6 and 05g(x)dx=2.

Explanation

Given Information:

The provided function is 05[f(x)+g(x)]dx and also 05f(x)dx=6 and 05g(x)dx=2.

Formula used:

The property of definite integral when f and g is assumed to be continuous on closed interval [a,b], then,

ab[f(x)±g(x)]dx=abf(x)dx±abg(x)dx

Calculation:

Consider the integral,

05[f(x)+g(x)]dx

By using the property ab[f(x)±g(x)]dx=abf(x)dx±abg(x)</

(b)

To determine

To calculate: The definite integral of function 05[f(x)g(x)]dx by using the values 05f(x)dx=6 and 05g(x)dx=2.

(c)

To determine

To calculate: The definite integral of function 054f(x)dx by using the values 05f(x)dx=6 and 05g(x)dx=2.

(d)

To determine

To calculate: The definite integral of function 05[f(x)3g(x)] by using the values 05f(x)dx=6 and 05g(x)dx=2.

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