`f'(t) = 4/(1 + t^2), f(1) = 0` Find `f`.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

The general antiderivative of f' is

`f(t)=4arctan(t)+C,`

where C is any constant.

It must be f(1)=0, so C=-4arctan(1). acrctan(1) is `pi/4,` so the answer is

`f(t)=4arctan(t)-pi.`