Find the volume of the indicated region.
-the region that lies under the plane z = 6x + 9y and over the triangle with vertices at (1, 1), (2, 1), and (1, 2)
A) 16
B) 10
C) 20
D) 14

Question

Quizplus · Accepted Answer

The triangle lies in the xy-plane with vertices (1,1), (2,1), and (1,2). The area of this triangle is 0.5. The plane z = 6x + 9y gives the height above each point in the triangle. Integrating over the triangle, the volume is the integral of (6x + 9y) over the region, which evaluates to 10.

Find the Volume of the Indicated Region