Reducing it to three questions, because I'm pretty confident on the others.(adsbygoogle = window.adsbygoogle || []).push({});

9. Find the volume of the solid generated by revolving about the line x = -1, the region bounded by the curves y = -x^2 + 4x - 3 and y = 0.

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I graphed everything, and then translated the graph 1 to the right making it y=-(x-1)^2+4(x-1)-3 and y=0 rotated around the y-axis because this is easier for me.

So then, I should be able to do this with the shell method, and get [tex]\int_2^4 2x \pi (-(x-1)^2+4(x-1)-3)\,dx[/tex]

I don't think I'm right because this is negative

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10. Consider the region in the xy-plane between x = 0 and x=pi/2 bounded by y = 0 and y = sin x. Find the volume of the solid generated by revolving this region about the x-axis.

stuck here too

Honestly, I just am posting this because my answer seems to simple

[tex]\int_0^\pi/2 sin^2x\,dx [/tex]

11. Let R be the region bounded by y = 1/x, y = x^2, x = 0, and y = 2. Suppose R is revolved around the x-axis. Set up but do not evaluate the integrals for the volume of rotation using: a) the method of cylindrical shells; b) the method of circular disks.

Honestly don't know where to start

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# Homework Help: Disk and Shell Method (Ignore my other thread)

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