Question

find the anti derivative

Answer 1

\[f'(t) = \frac{ 4 }{ 1+t^2}\]

Answer 2

where f(1) = 0

Answer 3

Hmm, do you want to do it through integration?

Answer 4

yes

Answer 5

It looks like arctan.

Anyway, initially I would probably just use a trig function due to the \(1+x^2\)

Answer 6

I mean \(1+t^2\).

Answer 7

okay so 4(arctan) + c for starting

Answer 8

Yeah, if you're allowed to use that fact, then it would make things easy

Answer 9

okay so now how do I find c?

Answer 10

0 = 4(arctan(1))?

Answer 11

You use \(f(1)=0\).

Answer 12

So letting \(t=1\) and the whole thing \(=0\), you have an equation to find \(C\).

Answer 13

Alternatively you may use: \[
f(t) -f(1)= \int^t_1f'(x)~dx
\]