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bii17

  • 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
    • 3 years ago
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    what is wallis formula ?

  2. shubhamsrg
    • 3 years ago
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    nevermind, just substitute cost = u see if it helps.

  3. Spacelimbus
    • 3 years ago
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    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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