Answer
$$ y= x^4+3$$
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
$$ y= x^4+3$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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