109k views
0 votes
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

1 Answer

2 votes

Answer:

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.

User Ionut Achim
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories