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Math Help - Double Integral Help!

  1. #1
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    Double Integral Help!

    Hello people! I need help to evaluate the integral on the following attachment. The problem is number 5. An explanation will be much appreciated too.
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  2. #2
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    oops forgot to upload the image
    Attached Thumbnails Attached Thumbnails Double Integral Help!-2.jpg  
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  3. #3
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    Quote Originally Posted by aeubz View Post
    oops forgot to upload the image
    The integral with respect to y of x sin y is just -x cos y. x is treated like a constant ....
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  4. #4
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by mr fantastic View Post
    The integral with respect to y of x sin y is just -x cos y. x is treated like a constant ....
    \int_0^\pi \int_0^x x\sin{y}~dydx

    \int_0^\pi -x\cos{y}\bigg|^x_0~dx

    \int_0^\pi -x\cos{x} + x\cos{0}~dx

    \int_0^\pi (-x\cos{x} +x)~dx


    Next you going to need to use IBP

    \int^\pi_0 -x\cos{x}dx +\int^\pi_0 xdx

    -[x\sin{x} - \int^\pi_0 \sin{x}dx] +\frac{x^2}{2}

    -x\sin{x} - \cos{x} +\frac{x^2}{2}\bigg|^\pi_0
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