Chapter 5.3, Problem 47E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Using Properties of Definite Integrals Given ∫ 2 6 f ( x ) d x = 10 and ∫ 2 6 g ( x ) d x = − 2 , evaluate(a) ∫ 2 6 [ f ( x ) + g ( x ) ] d x . (b) ∫ 2 6 [ g ( x ) − f ( x ) ] d x . (c) ∫ 2 6 2 g ( x ) d x . (d) ∫ 2 6 3 f ( x ) d x .

(a)

To determine

To calculate: The definite integral 26(f(x)+g(x))dx using the provided values 26f(x)dx=10 and 26g(x)dx=2

Explanation

Given:

The provided values are

âˆ«26f(x)dx=10 and âˆ«26g(x)dx=âˆ’2

And the integral to be evaluated is

âˆ«26(f(x)+g(x))dx

Formula used:

If f(x) and g(x) are integrable on [a,b] then the function f(x)+g(x) are integrable on [a,b], and

âˆ«ab(f(x)+g(x))dx=âˆ«abf(x)dx+âˆ«abg(x)dx

Calculation:

âˆ«26(f(x)+g(x))dx

As the provided functions f(x) and g(x) are integrable on [2,6]

(b)

To determine

To calculate: The definite integral 26(g(x)f(x))dx using the provided values 26f(x)dx=10 and 26g(x)dx=2

(c)

To determine

To calculate: The definite integral 262g(x)dx using the provided values 26f(x)dx=10 and 26g(x)dx=2

(d)

To determine

To calculate: The definite integral 263f(x)dx using the provided values 26f(x)dx=10 and 26g(x)dx=2

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