Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 4 - Integration - 4.1 Exercises: 5

Answer

$ y $ = $ \frac{2}{5}x^{\frac{5}{2}} + C $

Work Step by Step

$\frac{dy}{dx} $ = $ x^{\frac{3}{2}}$ To get the original equation, we have to integrate the aforementioned differential equation. $y=\int dy=\int x^{\frac{3}{2}} dx$ = $\frac{x^{{\frac{3}{2}}+1}}{{\frac{3}{2}}+1} + C $ = $ \frac{x^{\frac{5}{2}}}{\frac{5}{2}} + C $ = $ \frac{2x^{\frac{5}{2}}}{5} + C $ = $ \frac{2}{5}x^{\frac{5}{2}} + C $ Hence, $ y $ = $ \frac{2}{5}x^{\frac{5}{2}} + C $ The result checks out by differentiation.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After 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.