Question

I'm stuck on this problem, and am not sure where I'm going wrong, but I can't get the antiderivative! Would someone be willing to walk me through my error, and help me understand how to get to the answer?

**I will post the problem as the first comment

Any and all help is greatly appreciated!

Answer 1

The problem:
\[\int\limits_{0}^{\pi}\sec^2(\frac{t}{4})dt\] ; Evaluate.

Answer 2

\[substitute~\frac{ t }{ 4 }=x,t=4x,dt=4~dx,when t=0,x=0,t=\pi,x=\frac{ \pi }{ 4 }\]
\[I=4\int\limits_{0}^{\frac{ \pi }{ 4 }}\sec ^2x~dx=4 \tan x~|0 \to~\frac{ \pi }{ 4 }=4\left( \tan \frac{ \pi }{ 4 }-\tan 0 \right)\]
=?

Answer 3

Ah... my bad. Your comment illuminated a critical flaw in my work: I took the antiderivative of t/4, not the derivative to get "du" (or dx)... My bad. The answer is 4:)