Sketching and Calculating the Volume of Solid E

[kieranl]

Homework Statement

Sketch the solid E bounded by the cylinder x = y^2 and the planes z = 3 and x + z = 1, and write down its analytic expression. Then, use a triple integral to find the volume of E.

The Attempt at a Solution

Was wondering if someone could have a go at drawing this sketch? In mine, I thought i did it right but can't seem to obtain an enclosed surface. If x+z=1 was rather x-z=1 i would be able to but can't so far?

 

[HallsofIvy]

The plane x+ z= 1 crosses the plane z= 3 when x+ 3= 1 or the line x= -2, z= 3, y= t. It crosses the cylinder $x= y^2$ in the line $x= t^2$, $y= t$, $z= 1- x= 1- t^2$.

I wonder if you weren't confusing $x= y^2$ with the $y= x^3$.

 

[Pinu7]

I don't think you NEED to graph this.

y=(plus/minus) sqrt(x)

If that helps.

The range is x>0, so sqrt(x) is real.

If x>0, which is on top, z=3 or z=1-x?


EDIt: Is there an upper bound on x?

 

[kieranl]

wat i have done is drawn the cylinder x = y^2 in the x-y plane and extended it along the z plane. Then i drew the z=3 plane and then drew a line z=1-x and it extended it along the y plane. But this does not end up enclosing a solid

 

[Pinu7]

wat i have done is drawn the cylinder x = y^2 in the x-y plane and extended it along the z plane. Then i drew the z=3 plane and then drew a line z=1-x and it extended it along the y plane. But this does not end up enclosing a solid

You are right, I think. There must be an upper x-limit for this to be a solid. Maybe, you have accidentally skipped some information.