Calc
posted by Erica on .
Find the integral from ∞ to 1 of 1/(1+x²) dx.
I started working the problem out, and so far I got the lim as z→∞ of [arctan (1)  arctan (z)].
I'm a little bit confused exactly what is means when you plug ∞ into z, and how to solve the problem from here.
Thank you!

The indefinite integral is arctan x, as you have already indicated.
arctan(infinity), the angle that has a tangent of infinity, is (3/2)*pi
arctan(1) = (7/8)*(2 pi) = (7/4)pi
That makes the answer pi/4