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Math Help - Help with double/iterated integrals please

  1. #1
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    Help with double/iterated integrals please

    Hey guys. I'm having trouble with 3 questions:
    1. I(0->pi/2) I(0->cos(theta)) e^(sin(theta)) dr d(theta)...evaluate

    I get as far as I(0->pi/2) cos(theta) e^(sin(theta)) d(theta)...and then, I guess you have to use integration by parts, but no matter how I try to set it up I end up with something complicated.

    2. I(0->1) I(3y->y) e^(x^2) dxdy...evaluate the integral by reversing the order of integration.

    Same problem as #1.

    Any degree of help is appreciated. Thanks!
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  2. #2
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    Here is the first one.
    Use the substitution t=sin theta
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  3. #3
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    Quote Originally Posted by ParadigmShift View Post

    2. I(0->1) I(3y->y) e^(x^2) dxdy...evaluate the integral by reversing the order of integration.
    You are integrating the the region:

    R = {(x,y) | 0<=y<=1 and y<=x<=3y} ---> See below

    In order to change order we need to find the top and bottom curves.

    The top curve is y=1 and bottom is y=(1/3)x

    Hence we can think of the region alternatively as,

    R = {(x,y) | 0<=x<=3 and (1/3)x<=y<=1}
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  4. #4
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    Quote Originally Posted by ThePerfectHacker View Post
    Here is the first one.
    Use the substitution t=sin theta
    I had already gotten as far as your partial solution shows. But I think from that point I start to do it incorrectly. You mean I have to let t=sin(th) and THEN use integration by parts, because that's what I've been trying to do to no avail. I still need a nudge

    Thanks for your help on the second one. It's been a long time since I did calc II so I'm rusty (plus I'm generally bad at math).
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  5. #5
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    Quote Originally Posted by ParadigmShift View Post
    I had already gotten as far as your partial solution shows. But I think from that point I start to do it incorrectly. You mean I have to let t=sin(th) and THEN use integration by parts, because that's what I've been trying to do to no avail. I still need a nudge

    Thanks for your help on the second one. It's been a long time since I did calc II so I'm rusty (plus I'm generally bad at math).
    Here.
    Attached Thumbnails Attached Thumbnails Help with double/iterated integrals please-picture28.gif  
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