Question

our topic is application of improper integrals: bounded by y = 1 / x^2 + 4 and the x-axis. The answer is pi/2, i want to know how. thanks

Answer 1

because you can integrate this in reliance on the identity tan^2 + 1 = sec^2

and so you make the sub here of x = 2 tan theta
dx = 2 sec^2 theta

do it and you end up with a pretty simple answer

you integrate -inf to inf, and note that as theta --> inf, tan-1(inf) --> ?!?!?

Answer 2

hey thanks!