Asked by Ashley
Find the volume of the solid given by rotating the region bounded by the curves y=x^2, x=1, x=2, and y=0 around the y-axis
a) Use the shell method
b) Use the washer method. Be careful with the radius of the washer at different y.
a) Use the shell method
b) Use the washer method. Be careful with the radius of the washer at different y.
Answers
Answered by
Steve
shells of thickness dx:
v = ∫[1,2] 2πrh dx
where r=x and h=y=x^2
v = ∫[1,2] 2πx*x^2 dx = 15π/2
washers of thickness dy -- the curved portion plus a cylinder 1 unit high with radii 1 and 2:
v = 3π + ∫[1,4] π(R^2-r^2) dy = 15π/2
where R=2 and r=x=√y
v = ∫[1,4] π(4-y) dy =
v = ∫[1,2] 2πrh dx
where r=x and h=y=x^2
v = ∫[1,2] 2πx*x^2 dx = 15π/2
washers of thickness dy -- the curved portion plus a cylinder 1 unit high with radii 1 and 2:
v = 3π + ∫[1,4] π(R^2-r^2) dy = 15π/2
where R=2 and r=x=√y
v = ∫[1,4] π(4-y) dy =
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