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The region R is bounded by the curve y=sqrt(x)+5/sqrt(x) the x-axis and the lines x = 3, x = 4. Find the volume generated when R is rotated through four right-angles about the x-axis. Give your answer correct to the nearest integer.

The general formula for a volume of rotation is pi times the integral of y^2. The first step is to square y. this can be done by squaring the first term, squaring the last term and finding twice the product. Add all these answers together. Now integrate this firstly as an infinite intergration to get x+25/x+10. Now impose the limits and multiply by pi to give 65 units cubed.

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