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I'm trying to do my mathematical analysis homework but I have faced one struggle.

$$\iint_{\omega} y^2\,dx\,dy$$ where $\omega$ is bounded by the axis of abscissas and the first arch of the cycloid $$ \left\{ \begin{array}{c} x=a(t-\sin(t)) \\ y=a(1-\cos(t)) \end{array} \right. $$ where $0≤t≤2\pi$ and $a>0$.

What I found out is the graph itself:enter image description here And, let's say, I choose to integrate y from 0 to 2a and how can I express the function itself?

I need hints, how to create such an integral. Thank you!

Nehorai Elbaz
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Karagum
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  • Do you know Green's Formula ? https://en.wikipedia.org/wiki/Green%27s_theorem – Kelenner Sep 16 '17 at 11:58
  • @Kelenner No, I don't know it and the thing is that I can't use it. I need to create definite integral and found what the interval of this integral is. – Karagum Sep 16 '17 at 12:03

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