Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - Chapter Review Exercises - Page 278: 31


$$ y= x^4+3$$

Work Step by Step

Given$$ \frac{d y}{d x}=4 x^{3}, \quad y(1)=4$$ Since :\begin{align*} y&= \int 4x^3 dx\\ &= x^4+c \end{align*} at $x= 1,\ \ \ y= 4 $, then $c= 3$, hence $$ y= x^4+3$$
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