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 280: 50

Answer

\begin{array}{l} \frac{7+x^{3}}{3}=C \end{array}

Work Step by Step

\[ x^{2}=f^{\prime}(x) \] Integrate to get $f(x)$ \[ \begin{array}{l} \int x^{2} d x =f(x)\\ C+\frac{1}{3} x^{3}=f(x) \end{array} \] Given that the curve passes through (-1,2) Substitute $f(x)=-1, x=2$ and solve for $C$ \[ \begin{array}{c} \frac{1}{3}(-1)^{3}+C=2 \\ -\frac{1}{3}+C=2 \\ \frac{1}{3}+2=C\\ \frac{7}{3}=C \end{array} \]
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