Use the shell method to find the volume of the solid below the surface of revolution and above the xy-plane. The curve z = 4x − x2 in the xz-plane is revolved about the z-axis.

Q: 2. Sketch the graphs of y = x² - 6x + 12, x = 5, x-axis and y-axis. Shade the region bounded by the…

A: The given equation of the curve is: and

Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

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Q: Find the surface area of the object obtained by rotating x = Vy-6 2sys3 about the y-axis.

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Q: y2=x, y=x. What is the volume of the curve is rotated about the y-axis

A: According to the washer method volume of solid rotated around the y-axis is given by:

Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

A:

Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3