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anonymous

  • 4 years ago

How do you integrate (sin(x))^3 ?

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  1. anonymous
    • 4 years ago
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    I already looked at Wolfram and I don't want to use the reduction formula

  2. bahrom7893
    • 4 years ago
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    Sin*(Sin^2(x))

  3. bahrom7893
    • 4 years ago
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    Then: Sin*(1-Cos^2(x))

  4. bahrom7893
    • 4 years ago
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    That leads to Sin - Sin*Cos^2 split it into two integrals

  5. bahrom7893
    • 4 years ago
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    first one is easy, second one - integration by parts, then you go through the loop again

  6. bahrom7893
    • 4 years ago
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    I say reduction formula I think it's 1/2 something... is much easier

  7. anonymous
    • 4 years ago
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    ok I see what you want to do

  8. anonymous
    • 4 years ago
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    I've never been taught that reduction formula so I'd rather not use it yet

  9. bahrom7893
    • 4 years ago
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    remember that? Then at the end you get something like Int(Sin*Cos^2) = __________ - Int(Sin*Cos^2), then u add Int(Sin*Cos^2) to both sides and divide by two or whatever..

  10. anonymous
    • 4 years ago
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    yeah that makes sense I'll try it using your strategy

  11. anonymous
    • 4 years ago
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    I ended up using subsitution for the second part because it seemed easier I got (((cos(x))^3)/3) - cos(x) Thanks again for your help!

  12. TuringTest
    • 4 years ago
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    yes, subbing for the second part is way easier, it's practically udu already because it is cos^n(x)*(-sinx)

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