Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 279: 45



Work Step by Step

Given $$f''(x)= \sqrt{x}$$ integrate both sides \begin{align*} f'(x)&=\int x^{1/2}dx\\ &=\frac{2}{3}x^{3/2}+c_1 \end{align*} To find $f(x) $ \begin{align*} f(x)&=\int f'(x)dx\\ &=\int \left(\frac{2}{3}x^{3/2}+c_1\right)dx\\ &=\frac{4}{15}x^{5/2}+c_1x+c_2 \end{align*}
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