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Math Help - another integration problem

  1. #1
    Senior Member Sambit's Avatar
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    Question another integration problem

    evaluate  \int_0^1(\int_x^1 \frac{e^{-y}}{y} dy) dx
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  2. #2
    A Plied Mathematician
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    Change the order of integration. Makes things much easier! Draw the region carefully to get the new limits.
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  3. #3
    Senior Member Sambit's Avatar
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    if we reverse the order of  dx and  dy , the integration becomes  \int_0^1(\int_0^y \frac{e^{-y}}{y} dx) dy
    so the final answer comes to be  1 - \frac{1}{e} . thanks
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  4. #4
    A Plied Mathematician
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    You're welcome. Have a good one!
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