Is the Volume Calculation for the Bounded Solid Correct?

[Bob19]

I need to find the volume of solid bounded by the elliptic paraboloid z = 1 + (x-1)^2 + 4y^2, the planes x = 3 and y = 2 and the coordinate planes.


I claim that the solid called S is bounded above the square R = [0,3] x [0,2]

Thereby resulting in a volume V = 44.

Is that a correct assumption ?

Sincerely and best regards,

Bob

 

[Fermat]

I check your answers.