EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z = 8x2 + 8y2, above the xy-plane, and inside the cylinder x2 + y2 = 2x. SOLUTION The solid lies above the disk D whose boundary circle has equation x2 + y2 = 2x or, after completing the square,

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)

20

step-by-step explanation:

where is the figure