Answer
The integral diverges.
Work Step by Step
We have
$$
\int_{0}^{\infty} \sin x dx=-\cos x|_0^{\infty}
$$
Since $\lim_{x\to \infty }\cos x$ is undefined, the integral diverges.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 35
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