Answer
$$y= 2\sqrt{x}-1 $$
Work Step by Step
Given$$ \frac{d y}{d x}=x^{-1 / 2}, \quad y(1)=1$$
Since :\begin{align*}
y&= \int (x^{-1 / 2}) dx\\
&= 2\sqrt{x} +c
\end{align*}
at $x=1,\ \ \ y= 1 $, then $c= -1$, hence
$$y= 2\sqrt{x}-1 $$
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: 33
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