A curve in the $xy$-plane is given parametrically by $x(t) = e^{2t}, \quad y(t) = e^{2t} \sin(2t), \quad t \in [0, \pi/2].$ What is the length of this curve?
Ok, actually I know what to do, but I don't know how to do it because I can't get rid of the trigonometric term.
If it were $x(t) = e^{2t}\cos(t)$, I could have done it, but it's not so I can't get rid of the trigonometric term and integrate the expression.