The diagram shows the curve defined by parametric equations $\displaystyle x = t^{2} $ , $\displaystyle y = t^{3} $

for values of t between -3 and 3 find the shaded area.

I have drawn the diagram shows in my book and this my set up,

$\displaystyle \int^3_{-3} t^{3} \\\ 2t \\\ dt $

However when I compute this, I do not get the right answer. Is this the correct method?

thank you.

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