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Math Help - plz give me the formula of integration by parts

  1. #1
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    plz give me the formula of integration by parts

    i need to know the integration formula for double components like integration of u*v......plz suggest
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  2. #2
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    Re: plz give me the formula of integration by parts

    Just in case a picture helps...



    ... is lazy integration by parts, doing without u and v.



    ... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x.

    See here.

    The formula, of course, (one version, anyway) is

    \int u v'\ dx = uv - \int u' v\ dx

    But the important thing is to see how it depends entirely on working backwards through the product rule for differentiation.

    Also: Integration by parts - Wikipedia, the free encyclopedia


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    Don't integrate - balloontegrate!

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  3. #3
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    Re: plz give me the formula of integration by parts

    See google
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  4. #4
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    Re: plz give me the formula of integration by parts

    It's pretty easy to derive.

    The product rule says that, for two functions u and v in terms of x, \frac{d}{dx} (uv) = u \frac{dv}{dx} + v \frac{du}{dx}. Integrate both sides with respect to x to obtain

    uv = \int u \frac{dv}{dx} dx + \int v \frac{du}{dx} dx

    uv = \int u dv + \int v du

    Rearranging, we get the integration by parts formula, \int u dv = uv - \int v du (you can add an arbitrary constant).
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  5. #5
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    Re: plz give me the formula of integration by parts

    Hello, cooper607!

    I need to know the formula for integration by parts.

    \text{Formula: }\:\int u\,dv \;=\;uv - \int v\,du
    n . . . . . . . . . . . . . . \uparrow\qquad\quad\uparrow
    . . . . . . . . . . \text{"ultra-violet\; voodoo"}
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