how do i set this problem up?

Use the method of cylindrical shells to find the volume gener- ated by rotating the region bounded by the given curves about the y-axis. Sketch the region and a typical shell.

y=x^3, y=0, x=1; about y=1

Question

how do i set this problem up?

Use the method of cylindrical shells to find the volume gener- ated by rotating the region bounded by the given curves about the y-axis. Sketch the region and a typical shell.

y=x^3, y=0, x=1; about y=1

dumbcow · Answer

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volume using shell method
$$2\pi \int\limits radius*height$$
because its being rotated around horizontal axis...radius must be in terms of "y"
x = y^1/3
$$\rightarrow 2\pi \int\limits (1-y)(1-\sqrt[3]{y}) dy$$