Question

evaluate the integral from pie to 0 sec^2 theta d theta

Answer 1

CAUTION!: although the integration will yield tantheta....it is not cause tantheta suffers n discontinuity @ pi/2

Answer 2

Are you sure its not from 0 to pi?
In that case:
You have to break it up because sec(theta) has a discontinuity at pi/2.
So your integral becomes:
\[I=\int\limits_{0}^{\pi/2}\sec^2(\theta) d \theta+\int\limits_{\pi/2}^{\pi}\sec^2(\theta) d \theta\].
Then that has to become:
\[I=\lim_{ \alpha \rightarrow \pi/2^-} \int\limits_{0}^{\alpha}\sec^2(\theta)d \theta+\lim_{\beta \rightarrow \pi/2^+}\int\limits_{\beta}^{\pi}\sec^2(\theta) d \theta\].
So then evaluate your integrals. Then take the limits. This particular integral diverges.

Answer 3

sorry.. is from 0 to pie/4

Answer 4

Oh. In that case, its straight forward. Integral of sec^2(x) is tan(x) so you have tan(pi/4)-tan(0)=1.