Question

Evaluate the double integral by first identifying it as the volume of a solid.

Answer 1

Step 1:

The double integral is and region is .

Volume of the solid :

If , then the volume  of the solid that lies above the rectangle  and

below the surface is .

Therefore the double integral represents volume of the solid, below the surface

and above the rectangle .

From the definition of double integrals, .

.

Solution :

The double integral represents volume of the solid.

.