Describe volume bounded by x + y^2 = 4, z = 0, x = 0, and

[Smily]

Describe the volume bounded by the cylinder x + y^2 = 4 and the planes z = 0, x = 0, and y + z = 2 as:

. . .V = (Int) (Int) (Int) dz dx dy

...and as:

. . .V = (Int) (Int) (Int) dx dy dz

Note: "(Int)" indicates the integral symbol.

Can you help me to solve it, please? :roll:

 

[galactus]

Re: Describe volume bounded by x + y^2 = 4, z = 0, x = 0, an

Describe the volume bounded by the cylinder \(\displaystyle x + y^{2} = 4\) and the planes \(\displaystyle z = 0, \;\ x = 0, \;\ and \;\ y + z = 2\) as:

\(\displaystyle \L\\V = \int\int\int dz dx dy\)

...and as:

\(\displaystyle \L\\V = \int\int\int dx dy dz\)

I'll try one and you see if you can get the other.

\(\displaystyle \L\\\int_{0}^{2}\int_{0}^{4-y^{2}}\int_{0}^{2-y}dzdxdy\)