Answer
$$y= \tan x +1 $$
Work Step by Step
Given$$ \frac{d y}{d x}=\sec^2 x, \quad y(\pi/4)=2$$
Since :\begin{align*}
y&= \int (\sec^2 x) dx\\
&= \tan x +c
\end{align*}
at $x=\pi/4,\ \ \ y= 2 $, then $c= 1$, hence
$$y= \tan x +1 $$
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: 34
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