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Math Help - Volume by double integral

  1. #1
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    Volume by double integral

    We just started learning about nested integrals and this problem is way beyond me!!!!

    I need to determine the volume under the f(x,y) = x^2 + y^2 and above the triangle where
    y < or equal to x and x is > or equal to 0 but less than or equal to 9


    I realize the first function is a circle and that the bounds for x are 0 and 9. I assume my function to integrate would be ( x^2 + y^2 - 1/2xy) dy dx but ........

    Thanks to all of you helpful folks. I feel bad that I am not able to render math help of this caliber. I am providing free English tutoring at our junior college in an effort to continue the good work that I have found on this forum. Frostking
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  2. #2
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    All you integrate is f(x,y). Just need to worry about limits. Sketch the area first. You should find it clear that x ranges from 0 to 9, but what about x? Well it ranges from y=0 on the lower boundary to y=x on the upper boundary, so integrate from 0 to x but inside the x integral (so dydx). Or integrate y from 0 to 9 and x from y to 1 dxdy. ^_^
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