Thread: 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

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.

i cant imagine it

I would approach it like this:
where

the main problem is how to know how y^2+ z^2= x looks like
i only know how y^2+ x^2= z

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