Homework SourseFind the volume of the solid generated by revolving the regi
Find the volume of the solid generated by revolving the region enclosed
by y = x^2-1
x = 1; x = 4 and y = 0
(a) about x-axis.
(b) about y-axis.
(c) about x = 4
(d) about y = 1.
by y = x^2-1
x = 1; x = 4 and y = 0
(a) about x-axis.
(b) about y-axis.
(c) about x = 4
(d) about y = 1.
Solution
After squaring and integrating R : 2pi(-e^-2 + 1)
After plugging in the limits and subtracting, I got: 2pi(e^-2 + 1) INT pi[ e^(-1/4x )]^2 dx= INT pi [ e^(-x/2)dx] = -2pi* e^(-x/2) | (0,4)
Plug in x=4 first, then 0, then subtract:
-2pi( e^ -2 - e^0)
= -2pi ( e^-2 -1)
= 2pi- 2pi/e^2
