find the volume inclosed by z=0 x=y and y^2+z^2=x

i am having trouble drawing it

i know i should look on th shadow of it on the x-y plane and integrate by it

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- May 24th 2011, 04:31 AMtransgalacticvolume integral with 3 formulas mmn 15 3a
find the volume inclosed by z=0 x=y and y^2+z^2=x

i am having trouble drawing it

i know i should look on th shadow of it on the x-y plane and integrate by it - May 24th 2011, 04:39 AMHallsofIvy
No, you shouldn't. y^2+ z^2= x is a paraboloid with axis along the x-axis, not the y-axis. For this problem you should project onto the yz-plane.

Or, you can just "change" the problem- swap x and y and find the voume of the region bounded by x= 0, z= y, and z= x^2+ y^2. For that, you project onto the xy-plane. - May 24th 2011, 06:30 AMtransgalactic
i cant imagine it

- May 24th 2011, 09:23 AMMondreus
I would approach it like this:

$\displaystyle \iint_D\int_{y^2+z^2}^{y}dxdydz$ where $\displaystyle D: y^2+z^2\leq y; z\geq0$ - May 24th 2011, 11:33 AMtransgalactic
the main problem is how to know how y^2+ z^2= x looks like

i only know how y^2+ x^2= z - May 24th 2011, 12:49 PMtransgalactic
- Jun 25th 2011, 02:45 PMtransgalacticRe: volume integral with 3 formulas mmn 15 3a
i can project on every plane i want to and build the integral appropriatly

i jast cant imagine this shape

if i can find out how the shape looks like

then it will solve it very fast

but imaganening a parabaloid cutting x=0 plane and z=0

is very hard thing to draw and imagine