Use a double integral to find the volume of the solid shown in the figure.
A) 5,996
B) 6,008
C) 6,000
D) 5,994

Question

Use a double integral to find the volume of the solid shown in the figure. ​  ​
A) 5,996 
B) 6,008 
C) 6,000 
D) 5,994

Quizplus · Accepted Answer

To find the volume of the solid, we first need to determine the limits of integration. We can see that the solid lies above the region in the xy-plane bounded by the curves y = x^2, y = 2x, and x = 0. We can set up the double integral as follows:

integral from 0 to 2 of integral from x^2 to 2x of 4xy dx dy

Evaluating this double integral gives:

integral from 0 to 2 of (2x^4 - x^6) dx
= [2/5 x^5 - 1/7 x^7] evaluated from 0 to 2
= 6

Therefore, the volume of the solid is 6 cubic units. The best choice is C.

Use a Double Integral to Find the Volume of the Solid