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bii17

  • 2 years ago

integrate (x)(cos^3 x) dx

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  1. sirm3d
    • 2 years ago
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    do you know the reduction formula for \[\int \cos^n x \,\mathrm dx\]

  2. bii17
    • 2 years ago
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    reduction?? nope...

  3. matricked
    • 2 years ago
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    first simplify cos^3 x in terms of cosine of 3x and x and then integrate by parts

  4. matricked
    • 2 years ago
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    i don't think here u should use reduction formula

  5. bii17
    • 2 years ago
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    its \[\cos ^3 x\] .. where did u get 3x and x @matricked

  6. matricked
    • 2 years ago
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    use cos3x =4 cos^3 (x) - 3cos x

  7. sirm3d
    • 2 years ago
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    why not? it solves the problem too, but the solution may not be attractive to @bii17

  8. matricked
    • 2 years ago
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    i mean use cos^3 (x) =1/4 *(cos3x +3cosx)

  9. bii17
    • 2 years ago
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    oh okay.. then what will happen next ? @matricked

  10. matricked
    • 2 years ago
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    and then use by parts

  11. bii17
    • 2 years ago
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    \[1/4 [x(\cos 3x + 3\cos x)]dx\] is this correct? @matricked

  12. matricked
    • 2 years ago
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    yup

  13. bii17
    • 2 years ago
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    so there will be u and du den dv and v... i used Dv as cos 3x dx the V will be 1/3 sin 3x ???

  14. matricked
    • 2 years ago
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    for both integration of 1/4 *xcos3x take x as the first function

  15. bii17
    • 2 years ago
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    i get it.. thanks a lot :) @matricked

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