# volume integral with 3 formulas mmn 15 3a

• May 24th 2011, 04:31 AM
transgalactic
volume 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 AM
HallsofIvy
Quote:

Originally Posted by transgalactic
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

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 AM
transgalactic
i cant imagine it
• May 24th 2011, 09:23 AM
Mondreus
I would approach it like this:
$\iint_D\int_{y^2+z^2}^{y}dxdydz$ where $D: y^2+z^2\leq y; z\geq0$
• May 24th 2011, 11:33 AM
transgalactic
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 PM
transgalactic
• June 25th 2011, 02:45 PM
transgalactic
Re: volume integral with 3 formulas mmn 15 3a
Quote:

Originally Posted by HallsofIvy
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.

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