Revolve the region under the curve y= x^1/3 on the interval [0, 8] about the x-axis. The resulting volume is,?

Question

a. 16pi/3

b. 64pi/5

c. 96pi/5

d. 729pi/5

e. 384pi/7

f. 640pi/7

g. 6561pi/7

h. 2560pi/9

i. 10240pi/11

j. none of these

Answer 1

V = Int pi (y^2) dx between 0 and 8 =
pi Int x^2/3 dx =3/5 pi( 8^5/3) = 96pi/5 (c)