How to Integrate Parametric Curves With Algebraic Coefficient?

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I have researched all over the place to get answers to this question; albeit to no avail. Most information that I could find focused on simple sin / cosine values - as such I make this request for help.

I have this information:

x = acos3t , y = asint, 0 ≤ t ≤ pi/6

I need to integrate this between limits of a and 0. I used the general formula for integrating parametrics albeit the answer seems to go on forever. I can't seem to manipulate the answer to look like the original and then set that part to I (if that makes sense).

A photo of the question is attached if that helps. Check here.

Many thanks to anyone who helps.

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Hint: $$\int_0^ay\,\mathrm{d}x=\int_0^ay\frac{\mathrm{d}x}{\mathrm{d}t}\,\mathrm{d}t=\int_0^a(a\sin{(t)})(-3a\sin{(3t)})\,\mathrm{d}t$$