   Chapter 8.8, Problem 87E ### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

#### Solutions

Chapter
Section ### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Comparing Integrals(a) Show that ∫ − ∞ ∞ sin x   d x diverges.(b) Show that lim a → ∞ ∫ − a a sin x   d x = 0 .(c) What do parts (a) and (b) show about the definition of improper integrals?

(a)

To determine

To prove: The integral sinxdx diverges.

Explanation

Given: sinxdx

Formula used:

sinxdx=cosx+c

The limit formula for continuous functionis

limxcf(x)=f(c)

Proof:

The given integral can be solved as given below.

sinxdx=0sinxdx+0sinxdx=limaa0sinxdx+lim

(b)

To determine

To prove: The limit limaaasinxdx=0.

(c)

To determine
The information about improper integrals as given by parts (a) and (b).

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