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.
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