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Math Help - integration wrt y and x

  1. #1
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    integration wrt y and x

    Question asks:
    A region in the xy plane is bounded by the lines y = 1 and x= 1, and the curve y = e^x.

    If the question was as above but without y=1 then I can just integrate e^x. But even then what would be the boundary values? -10 to 1. -100 to 1?

    Then would I integrate with respect to y to deal with the y=1 bit. Then I would have to:

    y=e^x
    lny = x ie I integrate x = lny. But we haven't covered this form of integration in the course yet so I doubt if this is the correct way to go.

    Maybe the solution is a lot simpler - but I can't see how to solve. Can anyone help?

    Angus
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  2. #2
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    Re: integration wrt y and x

    Quote Originally Posted by angypangy View Post
    Question asks:
    A region in the xy plane is bounded by the lines y = 1 and x= 1, and the curve y = e^x.

    If the question was as above but without y=1 then I can just integrate e^x. But even then what would be the boundary values? -10 to 1. -100 to 1?

    Then would I integrate with respect to y to deal with the y=1 bit. Then I would have to:

    y=e^x
    lny = x ie I integrate x = lny. But we haven't covered this form of integration in the course yet so I doubt if this is the correct way to go.

    Maybe the solution is a lot simpler - but I can't see how to solve. Can anyone help?

    Angus
    It's the same area as the area bounded by the function \displaystyle y = e^x - 1, the \displaystyle x axis and \displaystyle x = 1.
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