Mathematics, 09.02.2022 14:00 imsatyam9365

Volumes of Revolution: 1. Find the volume V of the solid generated by revolving the region between the curves y=1/x, y=0, x=1, x=3 about the y axis.

2. find the volume of the solid formed by revolving the region bound by x^2+y^3=4 and x=0 and x=2 and y=0 about the y axis

3. The base of a certain solid is the region enclosed between the curves y=sin(x), y=0, x=π/4, x=3π/4, and every cross section perpendicular to the x axis is a square with one side across the base. Find the volume V of the solid.

4. Let Vx and Vy be the volumes of the solids obtained by revolving the region enclosed by y=1/x, y=0, x=1/2 and x=b, (b>1/2) about the x and y axes respectively. Is there a value for b for which Vx=Vy? (If there are multiple values, enter any one of them, if there are no values, enter 0).

I'm more interested in learning how to solve these problems than just getting the answer. Thanks!

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Volumes of Revolution: 1. Find the volume V of the solid generated by revolving the region between...