Thread: Area under Curve

1. Area under Curve

Find the area under the curve y = sec^2(x) between x=0 and x=(pi).

I tried the integral for sec^2(x) which is tan(x) but with the boundaries of x=0 and Pi I get 0 as my answer. Im guessing something needs to be done with the boundaries?
Your help will be greatly appreciated!

2. Notice that you have a problem $x = \tfrac{\pi}{2}$

3. Originally Posted by Bonki
Find the area under the curve y = sec^2(x) between x=0 and x=(pi).

I tried the integral for sec^2(x) which is tan(x) but with the boundaries of x=0 and Pi I get 0 as my answer. Im guessing something needs to be done with the boundaries?
Your help will be greatly appreciated!
note by the graph that this is an improper integral. you need to see if the first half of the integral converges or diverges.

$\lim_{b \to \frac{\pi}{2}} \int_0^b \sec^2{x} \, dx$