Question

Let C be parametrized by x = sin^2 t and y = sin t cos t for 0 ≤ t ≤ π/2. Find the length S of the curve C.

Answer 1

\[dS = \sqrt{x'(t)^2 + y'(t) ^2 }dt\]

integrate both sides ^_^

Answer 2

... with limits \(\displaystyle\int_0^{\pi/2}\cdots\)

Answer 3

@SithsAndGiggles got an imaginary answer 0.602343+0.381073 i and its wrong.
x'=sin(2t) and y'=cos(2t) right?

Answer 4

yes. remeber the ID:\[\sin^2(x) + \cos^2(x) = 1\]

Answer 5

yeah but then I still dont know what I got wrong?