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Math Help - Volume by nested integrals

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    Volume by nested integrals

    I need to determine the volume of the region between the plane z= x and the surface z = x^2 and the planes y = 0 and y = 3. I think the outer integral would be for dy and 0 and 3 the bounds but I am not sure about much else, especially what do I use for my function??? x^2??
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    Quote Originally Posted by Frostking View Post
    I need to determine the volume of the region between the plane z= x and the surface z = x^2 and the planes y = 0 and y = 3. I think the outer integral would be for dy and 0 and 3 the bounds but I am not sure about much else, especially what do I use for my function??? x^2??
    z = x,\;\;z=x^2 are the two respective heights of the surfaces (they intersect at x=0,\, x = 1). If you draw them in the x-z plane you will see this. You are correct on your outer integral, the full integral is

    V = \int_0^3 \int _0^1 x - x^2 dx\,dy
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