Question

Use the region in the first quadrant bounded by √x, y=2 and the y-axis to determine the volume when the region is revolved around the line y = -2. Evaluate the integral.

A. 18.667
B. 17.97
C. 58.643
D. 150.796
E. 21.333
F. 32.436
G. 103.323
H. 27.4

Answer 1

The radius of each disk is given by r = y + 2, and the height of each disk is given by h = √x.

Therefore, we can write:

V = ∫[0,4] π(√x + 2)^2 dx

Evaluating this integral gives:

V = π(32/3 + 16√2)

So, the volume of the solid generated by revolving this region around y = -2 is approximately 58.643.

Therefore, the answer is C.