8. Which expression below is equal to

A.

B.

C.

D.

E.

 

Solution: The answer is A

 

The integral in question is the double integral of 4x3 over a plane region D, defined as,

The graph of D:

However, region D can be expressed differently, as follows:

The graph of D:

Thus, the double integral of 4x3 over the region D can be rewritten as,