How do I find f(pi)f(π) for f(x)= 3 int_0^x cos(t)/cos(t/2)+cos(2t)/cos(t/2) dtf(x)=3x0cos(t)cos(t2)+cos(2t)cos(t2)dt ?

1 Answer
May 26, 2018

4*sin(3/2pi)4sin(32π)

Explanation:

Using that
cos(t)+cos(2t)=2cos(t/2)cos(3/2t)cos(t)+cos(2t)=2cos(t2)cos(32t)
so your indefinite integral is given by
2int cos(3/2t)dt=4/3sin(3/2t)+C2cos(32t)dt=43sin(32t)+C
and our definite integral is given by
4sin(3/2pi)4sin(32π)