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Math Help - Iterated integral problem

  1. #1
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    Iterated integral problem

    Find the volume of the region that is under the graph of f(x,y) = x^2 + y^2 and above the triangle y less than or equal to x and x greater than or equal to 0 less than or equal to 1.

    I would appreciate an guidance you all are willing to give. These nested integrals are really hard for me to set up!!!! Frostking
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  2. #2
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    Quote Originally Posted by Frostking View Post
    Find the volume of the region that is under the graph of f(x,y) = x^2 + y^2 and above the triangle y less than or equal to x and x greater than or equal to 0 less than or equal to 1.

    I would appreciate an guidance you all are willing to give. These nested integrals are really hard for me to set up!!!! Frostking
    Tell me if this makes sense?

    \int_0^1 \int_0^x x^2+y^2 dy~ dx
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  3. #3
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    Nested integral question

    I see clearly that the bounds for x should be 0 to 1 and for y 0 to x. I also understand that you would use the function x^2 + y^2 but what still confuses me is how are we taking into account the area of the triangle???? Why do I not have to subtract 1/2 base times height from x^2 + y^2??? Thanks very much for your input. Frostking
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  4. #4
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    Quote Originally Posted by Frostking View Post
    I see clearly that the bounds for x should be 0 to 1 and for y 0 to x. I also understand that you would use the function x^2 + y^2 but what still confuses me is how are we taking into account the area of the triangle???? Why do I not have to subtract 1/2 base times height from x^2 + y^2??? Thanks very much for your input. Frostking
    The triangle is described by 0\leq y\leq x \text{ and }0\leq x\leq 1.
    That is it! You do not need to do anything else.
    The problem is not asking to find the area of the triangle, it is asking to integrate the function over the rectangle.
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