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Consider the region R bounded by the parabola f x 2x x and the line...

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Calculus

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Consider the region R bounded by the parabola f x 2x x and the line y x a Find the exact area between the parabola and the line in R Show your steps and explain your reasoning b Set up an integral for the volume of the solid obtained by rotating R around the line x 2 You do not need to evaluate the integral Notes Your explanation should include i a rough sketch of the solid of revolution or region to consider ii Label your solid and show the radius es iii Clearly state the method you are using and why and iv Clearly show and justify your steps for setting up your integral Your final integral should be clearly shown

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