Find the volume of the given solid.

Question

Under the surface
z = 7xy
and above the triangle with vertices
(1, 1), (4, 1), and (1, 2)

Answer 1

The hypotenuse of the base is the line

y = (7-x)/3

So, add up all the small solids with base dx dy and height z

v = ∫[1,4]∫[1,(7-x)/3] 7xy dy dx

Answer 2

36