sorry about the last post. How does the book get from
to a negative integral going from pi/2 to 3pi/2 cot(t) + integral going from 3pi/2 to 2pi cos(t)?
because
so they split the integral into two parts. the interval on which it is negative and the interval on which it is positive. on the interval the function was negative, they took the negative of the function (which is positive) for that interval and integrated it
ok, so did they figure out where the integral was positive or negative by graphing it?
yes, that's one way. another way is to solve for the function = 0, then test points in all the intervals to see if you get a negative or positive answer