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Thread: An Intergral Check

  1. #1
    Junior Member Selim's Avatar
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    An Intergral Check

    $\displaystyle \int x^n sin(x) * dx$ = ______________________ + $\displaystyle \int x^{n-1} cos(x) * dx$

    I want to just say sin(x), but that n should be a +1 and not minus or am I wrong? And,

    $\displaystyle Evaluate \int 5x * sin(x) * dx$

    Would you just pull the 5 out and call it a day or what?
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  2. #2
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    Quote Originally Posted by Selim View Post
    $\displaystyle \int x^n sin(x) * dx$ = ______________________ + $\displaystyle \int x^{n-1} cos(x) * dx$

    I want to just say sin(x), but that n should be a +1 and not minus or am I wrong? And,

    $\displaystyle Evaluate \int 5x * sin(x) * dx$

    Would you just pull the 5 out and call it a day or what?
    in the blank cos(x) will come as it is the integration of sin(x). in ur second question as u said simply pull out 5 and integrate by parts.
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  3. #3
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    Quote Originally Posted by Selim View Post
    $\displaystyle \int x^n sin(x) * dx$ = ______________________ + $\displaystyle \int x^{n-1} cos(x) * dx$

    I want to just say sin(x), but that n should be a +1 and not minus or am I wrong? And,

    $\displaystyle Evaluate \int 5x * sin(x) * dx$

    Would you just pull the 5 out and call it a day or what?
    Using integration by parts

    Let $\displaystyle u = x^n$ so that $\displaystyle du = nx^{n - 1}$

    Let $\displaystyle dv = \sin{x}$ so that $\displaystyle v = -\cos{x}$.


    Then $\displaystyle \int{x^n\sin{x}\,dx} = -x^n\cos{x} - \int{-nx^{n - 1}\cos{x}\,dx}$

    $\displaystyle = -x^n\cos{x} + n\int{x^{n - 1}\cos{x}\,dx}$.
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  4. #4
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    never mind
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