Question

Find the volume of the region bounded above by the paraboloid z equals 3 x squared plus y squared and below by the square R: minus 1 less than or equals x less than or equals 1 comma negative 1 less than or equals y less than or equals 1.

Answer 1

V=5.333cubit unit

Explanation:

this problem question, we are required to evaluate the volume of the region bounded by the paraboloid z = f(x, y) = 3x² + y² and the square r: -1≤ x ≤ 1, -1 ≤ y ≤ 1

The question can be interpreted as z = f(x, y) = 3x² + y² and the square r: -1≤ x ≤ 1, -1 ≤ y ≤ 1 and we are told to evaluate the volume of the region bounded by the given paraboloid z

The volume V of integral evaluated along the limits of x and y for the 2-D figure, can be evaluated using the expression below

V = ∫∫ f(x, y) dx dy then we can now substitute and integrate accordingly.

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION: