Find the volume of the solid obtained by revolving the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=x, y=sqrt(x); about x=2

Q: 1. Find the volume generated by revolving about the x-axis of the area bounded by the curve y = 6x -…

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Q: The graph of the derivative f'(x) of f(x) is shown. Compute the total change of f(x) over the given…

A: Graph of f'(x) vs x is given. Here, f'(x)=∆f∆x Therefore, change in f(x) will be, ∆f=f'(x)·∆x It…

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: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

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Q: Find the area of the surface generated by revolving the given curve about the x-axis. y = 3x, 0 < x…

A: We are given a curve y=f(x) and limits with respect to the variable x, and we are supposed to…