# 454CHAPTER 6Applications of Integration23-7 Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curvesabout the y-axis.3. y x, y = 0, x= 14. y x, y = 0, x= 1, x = 225. у %3D е*, у 3D0, х3D 0, х%3D 16. у 3 4х — х*, у%3D х7. y x2, y 6x - 2x28. Let V be the volume of the solid obtained by rotating aboutthe y-axis the region bounded by y = vx and y x2. FindV both by slicing and by cylindrical shells. In both casesdraw a diagram to explain your method.

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Step 1

It is given that the curves are f(x) = x2 and g(x) = 6x–2x2 bounded about the y-axis.

Find the intersection of the two curves by equating each other as follows.

Step 2

Integrate the function using the cylindrical...

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