Question 7

At first I thought it was polar co-ordinates but it was parametric so I used the arc length formula to try and find the length of the curve in ONE of the quadrants. I would later times this by 4 to get the length of the curve all together. So arc length = $\displaystyle \int{\sqrt{\frac{dx}{dt}^{2}+\frac{dy}{dt}^{2}}}dt$

so after lots of cancelling and using everybody's favourite trig identity sin^2(t) + cos^2(t) = 1 I get it down to

$\displaystyle 3a\int{sint cos t}dt$

Okay now use a substitution of u = sint

to get $\displaystyle \frac{3a}{2} sin^{2}t$ but where are the limits I need to use to get this done? Can someone show me what the limits I need to use are?

Thanks

NOTE using t instead of theta