Find the volume of the solid bounded above by the surface z = f(x, y)
And below by the plane region R. ; R is the triangle with vertices (0, 0), (5, 0) and (0, 5).

Question

Find the volume of the solid bounded above by the surface z = f(x, y)
And below by the plane region R.  ; R is the triangle with vertices (0, 0), (5, 0) and (0, 5).

Quizplus · Accepted Answer

By using the double integral, we can calculate the volume of the solid region as follows:
∫∫Rf(x,y) dA
Here, R is the triangle with vertices (0,0), (5,0), and (0,5).
The equation of the plane containing this triangle is z=0, which is the lower boundary of the region.
Thus, we can write the integral as:
∫[0,5]∫[0,5-x]f(x,y) dy dx
Therefore, option A is the correct answer. Neither B nor C is correct.

Find the Volume of the Solid Bounded Above by the Surface