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Math Help - integration question, please help! pic included

  1. #1
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    integration question, please help! pic included

    Hi everyone, I'm having some trouble doing this question that involves reversing the order of equations (so that I guess you do dxdy first vs doing the initial dydx).

    Here is the question:

    Can anyone tell me what the graph would look like too? What areas would be shaded? I came up with something below...



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  2. #2
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    Quote Originally Posted by finalfantasy View Post
    Hi everyone, I'm having some trouble doing this question that involves reversing the order of equations (so that I guess you do dxdy first vs doing the initial dydx).

    Here is the question:

    Can anyone tell me what the graph would look like too? What areas would be shaded? I came up with something below...



    That is the same as
    3\left[\int_{x= -1}^\frac{1}{2}(x+ y) dydx- \int_{x= \frac{1}{2}}^1 (x+ y) dy dx\right]

    Notice the "-" between the two integrals. That is because the two boundaries cross as x= 1/2.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    That is the same as
    3\left[\int_{x= -1}^\frac{1}{2}(x+ y) dydx- \int_{x= \frac{1}{2}}^1 (x+ y) dy dx\right]

    Notice the "-" between the two integrals. That is because the two boundaries cross as x= 1/2.

    Hi, thank you for your response!

    I was told by my friend you need to subtract a triangle part from another and this seems to be what he was talking about.


    So how would I solve that integral? Is my idea of dividing the bigger triangle in half to solve for its area, solving the 2 parts of the smaller triangle and subtracting them both a good idea?

    Also, for your integrals I have to do reverse the order of integration, so I have to use horizontal sections first instead of vertical.

    Thank you!
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