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

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1. shubhamsrg

what is wallis formula ?

2. shubhamsrg

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

3. anonymous

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.

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