Using washers:
∫01 π [(1-x)2 - (1-√x)2]dx
= π ∫01 [1- 2x + x2 - 1 + 2√x - x]dx
= π ∫01 [x2 - 3x + 2√x]dx
= π [ 1/3x3 - 3/2x2 + 4/3x3/2]01 = π/6
Using shells:
2π ∫01 [(y - y2)(1 - y)]dy
= 2π ∫01 [y3 - 2y2 + y]dy
= 2π [ 1/4y4 - 2/3y3 +1/2y2]01 = π/6
Josh F.
tutor
that is the HEIGHT of each cylinder (r = 1 - y) -- solve for x in terms of y for each function, then subtract the x-coordinate on the left from the one on the right: y - y^2
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03/30/21
Hung N.
i have question on shell: why r= y-y^203/30/21