Volume of a solid bounded by a surface and planes using change of variables

[e^x]

Find the volume of the solid bounded by the surface z = 5 + (x-4)^2 + 2y and the planes x = 3, y =4, and the coordinate planes. (use a change of variables).

I need help getting started... what are my change of variables (u and v)?

 

[BigBeachBanana]

Find the volume of the solid bounded by the surface z = 5 + (x-4)^2 + 2y and the planes x = 3, y =4, and the coordinate planes. (use a change of variables).

I need help getting started... what are my change of variables (u and v)?

Before you can determine the appropriate change of variables, you need to figure out the bounds of the region R.
$$V=\iint_{R}5+(x-4)^2+2y\,dR$$

 

[e^x]

Before you can determine the appropriate change of variables, you need to figure out the bounds of the region R.
$$V=\iint_{R}5+(x-4)^2+2y\,dR$$

Okay, so are the bounds 0 <= y <= 4 and 0<= x<= 3? What now? How do i use that info to find u and v?

 

[BigBeachBanana]

Okay, so are the bounds 0 <= y <= 4 and 0<= x<= 3? What now? How do i use that info to find u and v?

Correct, but since the region R is a nice rectangular region, there's no need to use the change of variables. Is this a requirement?

 

[e^x]

Correct, but since the region R is a nice rectangular region, there's no need to use the change of variables. Is this a requirement?

yes, but I'm also confused how it's relevant so I'll wait and ask my teacher about it

 

[BigBeachBanana]

yes, but I'm also confused how it's relevant so I'll wait and ask my teacher about it

I mean you could set $u=x$ and $v=y$. You'll find that the Jacobian is 1, and it doesn't make the integration any easier.