Question

Find the volume of the solid in 3 r 3 bounded by y=x2 y = x 2 , x=y2 x = y 2 , z=x y 12 z = x y 12 , and z=0 z = 0 .

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a) 4 units³
b) 8 units³
c) 2 units³
d) 16 units³

Answer 1

To find the volume of the solid bounded by the given equations, set up a triple integral in Cartesian coordinates with appropriate limits of integration. The evaluated integral yields a volume of 2 units³.

Step-by-step explanation:

To find the volume of the solid bounded by the given equations, we need to set up a triple integral in Cartesian coordinates. The limits of integration for each variable will be determined by the intersection points of the curves.

The volume is given by:

V = ∭(0 to 1) ∭(y^2 to √y) ∭(0 to x*y/12) dz dy dx

After evaluating the integral, we find that the volume of the solid is 2 units³.