Find f if f'(x) =

Question

Find f if f'(x)=2cos(x)+sec²(x), -pi/2<pi/2, and f(pi/3)=5

I think I am supposed to find the antiderivative of f(x) and this is what I got

2sin(x)+tan(x)+C

I know its not simply putting 5 in for C, but I don't know what to do with the pi/3 part. If you can help, many thanks!

Answer 1

You got the antiderivative f(x) correctly.

Now plug in the constraint f(pi/3) = 5:

2sin(pi/3) + tan(pi/3) + C = 5

2sqrt(3)/2 + sqrt(3) + C = 5

C = 5 - 2sqrt(3)