Find the volume of the given solid. Enclosed by the paraboloidz = 7x2 + 4y2and the planesx = 0, y = 2, y = x, z = 0

The volume of the solid is:

Step-by-step explanation:

Consider the given paraboloid and the planes:

z = 7x² + 4y², x = 0, y = 2, y = x , z = 0

The region of  type -II can be expressed as:

D = {(x,y)| 0 ≤ x ≤ y, 0 ≤ y ≤ 2}

Suppose f(x,y) is continous  on type-I region D such that:

D = {(x,y) | a ≤ y  ≤ b, g₁(y)  ≤ x  ≤ g₂ (y) }

Then, we can compute the double integral as follows:

Thus, the volume of the solid is:

the 3rd on is correct

step-by-step explanation: