5). Find the volume of the solid of revolution generated by rotating the graph of y=8 lnx about the y-axis between y=0 and y=16

Question

Answer choices: 238.39pi, 246.39pi, 230.39pi, 214.39pi, 222.39pi
7). Find the area of the region bounded by y=√x-2, y=9, y=0, x=0

Answer 1

5. we will need x^2 for the square of the radius
y= 8lnx
y = ln x^8
or e^y = x^8
x^2 = e^(y/4)

V = π∫x^2 dy from 0 to 16
= π∫e^(y/4) dy from 0 to 16
= π [ 4 e^(y/4) ] from 0 to 16
= π ( 4e^4 - 4e^0)
= π (4e^4 - 4)
or
= 4π (e^4 - 1) or appr 214.39