Question

help, how do i get started evaluating this integral

Answer 1

use half angle formula for sin(2x)=2sinxcosx then cancel and integrate

Answer 2

Use the identity that sin(2x) = 2*sin(x)*cos(x) to rewrite the integrand (the stuff on the inside of the integral) into (2*sin(x)*cos(x))/(2*sin(x)). This all reduces to cos(x). From here, you can integrate cos(x) into sin(x) (note: since the derivative of sin(x) is cos(x), this means that the integral of cos(x) is sin(x)). I'll let you take it from here.

Answer 3

oh I forgot the small details that the integral of cos(x) is sin(x)+C where C is a constant, but that's trivial (ie not important) since you're evaluating this integral with limits. So the +C part will go away.