Answer
$$-\sqrt{7-t^2}+c .$$
Work Step by Step
Let $u=7-t^2$, then $du=-2tdt$, then
$$\int \frac{t}{\sqrt{7-t^2}}dt=-\frac{1}{2}\int \frac{1}{\sqrt{u}}du=-\frac{1}{2}\frac{\sqrt u}{1/2}+c\\=-\sqrt{7-t^2}+c .
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 81
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
