Use a double integral to find the volume of the solid shown in the figure.

Question

Quizplus · Accepted Answer

To find the volume of the solid, we need to integrate the function over the region of integration. The region of integration is given by the inequalities:

0 ≤ z ≤ x + y
0 ≤ x ≤ 2
0 ≤ y ≤ 2

So the integral is:

∫∫z dz dy dx = ∫∫(x + y) dy dx
                  = ∫0^2∫0^2 (x+y) dy dx
                  = ∫0^2 [xy + (y^2)/2]dy
                  = ∫0^2 [2x + 2]dx
                  = [x^2 + 2x]0^2
                  = 4

Therefore, the volume of the solid is 4 cubic units, and the correct option is C.

Use a Double Integral to Find the Volume of the Solid