Math

Let R be the region bounded by y = ln x, x-axis, and x = 3. Answer the following.

a) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about x = -2.

b) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about y = 4.

I am confused about this question as well. Could you please help me understand how to do this? I would greatly appreciate it!

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  1. (a) using shells,
    v = ∫[1,3] 2πrh dx
    where r = x+2 and h=y=ln(x)

    using discs,
    v = ∫[0,ln3] π(R^2-r^2) dy
    where R=5 and r=x+2=2+e^y

    (b) use the same ideas with a horizontal axis. Just keep in mind the volume of a disc (or a washer with a hole inside) and a cylinder. I usually try to do it both ways to make sure the answers agree.

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