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 =
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.
1 answer
1 answer