Question

using wallis formula solve:
integrate from negative pi over two to pi over two.
sin^3 t cos^10 t dt

Answer 1

what is wallis formula ?

Answer 2

nevermind, just substitute cost = u
see if it helps.

Answer 3

I have seen Wallis Formula before, unfortunately never in combination with a product of sin and cosine. Hence I would solve this integral using a substitution just as suggested:

\[\Large \int \sin^2(x)\sin(x)\cos^{10}(x)dx \\
\Large \int(1-\cos^2(x))\sin(x)\cos^{10}(x)dx \\
\\ \Large \int \sin(x)\cos^{10}(x)dx-\int\sin(x)\cos^{12}(x)dx \]

But since this answer isn't sufficient enough for this kind of problem, I will see if I can find again my notes/sites on Wallis Formula.