Quantity of antibodies at t=8

[KLS2111]

The rate at which antibodies are made is given by r(t) = t/ (1+t^2) thousands of antibodies per minute, where time, t, is in minutes. Assuming there are no antibodies at t=0, find the total quantity of antibodies in teh blood at the end of 8 minutes.

When I took the antideriv I came up with .5 ln (1+t^2).
I then plugged in 8 and came up with 2.087

I just wanted to know if I was on the right track with this. This particular problem had a multiple choice answer set of:
a. 1663 b 2387 c 2472 d 3895 e none of these

I tend to second guess myself when none of these is an option, so if someone could tell me if I was on track I would appreciate it.

 

[arthur ohlsten]

dR/dt=t/[1+t^2]
dR=t dt [1+t^2]
dR = 1/2 [2tdt/[1+t^2]] integrate
R=1/2 ln[1+t^2]+c
at t=0 R=0
0=1/2 ln 1 +c
c=0

R= 1/2 ln [1+t^2] evaluated at 0,8
R=1/2 ln[65] answer

I assume I am right as I agree with your approach

Arthur