Question

Find the volume of the solid bound by the planes z=0, x=1, x=2, y=-1,y=1 and the surface z=x2+y2?

Find the volume of the solid bound by the planes z=0, x=1, x=2, y=-1,y=1 and the surface z=`x^2+y^2`

Answer 1

`16/3`

Explanation:

`int_V dV = int_1^2 dx \ int_(-1)^1 dy \ int_0^(x^2 + y^2) dz`

`= int_1^2 dx \ int_(-1)^1 dy qquad x^2 + y^2`

`= int_1^2 dx qquad( x^2y + y^3/3)_(y = -1)^1`

`= int_1^2 dx qquad 2x^2 + 2/3`

`= ( (2x^3)/3 + (2x)/3 )_1^2 = 16/3`