13.2#6

I just had a mini question about this one, since I tried to evaluate it as
integral from 0 to 3/2pi with the integrand sin(t)cos(t) + 2t, I figured
the step before was the integrand of -3sin(t)cos(t)+4sin(t)cos(t) +2t. Are
you not allowed to perform algebra and reduce the coefficients the answers
were very close to each other.

Wrong answer (22.399..)
Correct answer (22.7066)

**********************
I only get the correct answer, and the wrong ones I can think of give me answers more wrong than yours, so it's hard for me to guess. How did you get the incorrect answer, maybe numerical integration on your calculator?  Btw, you can eyeball the vector field and figure out which function it's the gradient of.