Pure Mathematics

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In=∫ x^nSinx dx....with the limits π/2 and 0
i found that In would be equal to n(π/2)^(n-1) -n(n-1) In-2
how do i deduce the value of I4? where n=4

  • Pure Mathematics -

    you need to do integration by parts.

    ∫x^4 sinx dx
    du = 4x^3 dx

    dv = sinx dx
    v = -cosx

    ∫x^4 sinx = -x^4 cosx + 4∫x^3 cosx dx

    Now do all that again for each resulting integral, and the powers of x descends until you are left with just ∫sinx dx

    Then just add all the pieces together.

    Hmmm. I think you can save yourself some work. At x=0 all the terms with powers of x and sinx vanish.

    at x=π/2 all the terms with cosx vanish (odd powers of x).

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