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My Applications of Integrals course: https://www.kristakingmath.com/applications-of-integrals-course Learn how to find the volume of rotation around a line...

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The region in the second quadrant bounded above by the curve y = 16 - x2, below by the x-axis, and on the right by the y-axis, about the line x =. 1. Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by y= 2x and y = x^2 -3 about x= 6. 2. Find the...

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Oct 11, 2013 · calculus. Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 the x-axis,the y-axis,and the line x = 4.

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Find the volume V of the solid obtained by rotating the region bounded by y x 2 from M 408 L at University of Texas. Study Resources.

To find the volume of a solid of revolution by adding up a sequence of thin cylindrical shells, consider a region bounded above by z=f(x), below by z=g(x), on the left by the line x=a, and on the right by the line x=b. When the region is rotated about the z-axis, the resulting volume is given by V=2piint_a^bx[f(x)-g(x)]dx.

Use the shell method to find the volume of the solid generated by revolving the plane region bounded by y = x 2, y = 9, and x = 0 about the y-axis. Solution . Note . The volume of this solid was also found in Section 12.3 Part 3 using the slice method. For this solid, the slice and shell methods require roughly the same amount of work.

and the volume of the solid (of revolution) generated by Ris V = Z d c ˇ[f(y)]2dy: Example Find the volume of the solid generated by revolving the region bounded by the curve x= y2 and the lines y= 0, y= 2 and x= 0(the yaxis) about the yaxis. V = Z 2 0 ˇy4dy= ˇ y5 5 2 0 = ˇ 32 5: 8

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- Find the volume of the solid generated by rotating the region R bounded by the y axis, the line y = a, and the curve Find the volume of the solid generated by rotating the region bounded by y = x, y = 3 – x, and x = 4 around the line x = 5. Find the volume of the torus of radius a with inside radius b. Applets Volume By Disks Volume By Shells
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- The volume generated by the curve that revolved about the line is 181 cubic units. Solution

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