Consider the plane region bounded by y = e^x, x = 4, and y = 1.
Revolve this region about the line y = -1 and find the resulting volume of the solid.
(Please just provide the integral. That's all I'm having trouble with. Thanks.)
2007-02-01 15:51:21 · 3 answers · asked by Taryn 2 in Science & Mathematics ➔ Mathematics
y = e^x, and y = 1 intersect at (0,1) for the left boundary.
The right boundary is x = 4.
We want to use the washer method.
The larger radius R = (e^x - (-1)) = (e^x + 1)
The smaller radius r = (1 - (-1)) = 2
So the integral over [0,4] is
∫π(R² - r²)dx = π∫{(e^x + 1)² - 2²}dx
2007-02-01 16:02:10 · answer #1 · answered by Northstar 7 · 1⤊ 0⤋
The corresponding x for y=1 is x=0
As you ask only for the integral that would be
Integral between 0 and 4 of pi(1+e^x)^2dx
2007-02-02 07:47:00 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
Hint: ans = pi * integral from 0 to 4 of ( 2 + e^x )^2
= pi * [ 23 + 8 * e^4 + e^8 ] / 2
2007-02-02 00:49:50 · answer #3 · answered by 1988_Escort 3 · 0⤊ 0⤋