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Solution To solve: \int^{a}_{0}y^{4}\sqrt{a^{2}-y^{2}}dy (Utilising the Beta special function) Use the substitution y=a\sqrt{t} This implies t = \frac{y^{2}}{a^{2}} Change bounds and variable for y=0, t=0; for y=a, t = a2/a2 = 1 t=\frac{y^{2}}{a^{2}}\rightarrow \frac{a^{2}}{2y}dt=dy...

That did it thanks. Great skills! (I want them) I've still got something wrong. Subbing y=a\sqrt{t} into integrand: a^{4}t^{2}\sqrt{a^{2}(1-t)} Changing bounds and var (wrongly?): t=\frac{y^{2}}{a^{2}}\rightarrow \frac{a^{2}}{2y}dt=dy...

Thread now about latex syntax. I have a feeling I will need to use some Laplace symbols soon so it's great info. Ty

Homework Statement I have this incomplete Beta function question I need to solve using the Beta function. \int^{a}_{0}y^{4}\sqrt{a^{2}-y^{2}}dy Homework Equations Is there an obvious substitution which will help convert to a variant of Beta? Beta function and variants are in Beta_function...