# Let R be the region between the graphs of #y=1# and #y=sinx# from x=0 to x=pi/2, how do you find the volume of region R revolved about the x-axis?

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To find the volume of region (R) revolved about the x-axis, you can use the method of cylindrical shells. The formula for finding the volume using cylindrical shells is:

[ V = 2\pi \int_{a}^{b} x \cdot f(x) , dx ]

Where:

- (a) and (b) are the limits of integration, which in this case are (0) and (\frac{\pi}{2}).
- (f(x)) is the height of the shell at the point (x), which is the difference between the upper function ((y = \sin(x))) and the lower function ((y = 1)).
- (x) is the radius of the shell.

So, the volume of region (R) revolved about the x-axis can be found using:

[ V = 2\pi \int_{0}^{\frac{\pi}{2}} x \cdot (\sin(x) - 1) , dx ]

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