Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the...Asked by Mel
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis.
y = 9e^−x^2, y = 0, x = 0, x = 1
y = 9e^−x^2, y = 0, x = 0, x = 1
Answers
Answered by
oobleck
v = ∫[0,1] 2πrh dx
where r = x and h = y = 9e^(-x^2)
v = ∫[0,1] 2πx*9e^(-x^2) dx
use u = -x^2, du = -2x dx and you have
v = ∫[0,-1] -9πe^u du
where r = x and h = y = 9e^(-x^2)
v = ∫[0,1] 2πx*9e^(-x^2) dx
use u = -x^2, du = -2x dx and you have
v = ∫[0,-1] -9πe^u du