Asked by Lexi
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves x=y^(1/2), x=0, and y=4 about the x axis.
Answers
Answered by
Steve
v = ∫[0,4] 2πrh dy
where r=y and h=2-√y
v = ∫[0,4] 2πy(2-√y) dy = 32π/5
check, using discs
v = ∫[0,2] πr^2 dx
where r=y=x^2
v = ∫[0,2] πx^4 dx = 32π/5
where r=y and h=2-√y
v = ∫[0,4] 2πy(2-√y) dy = 32π/5
check, using discs
v = ∫[0,2] πr^2 dx
where r=y=x^2
v = ∫[0,2] πx^4 dx = 32π/5
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