(Technology Permitted) Let R be the region. bounded by y=In(x), y=0, x=e². a. Write but do not evaluate an integral expression for the area of region R. b. What is the volume of the solid generated when R is rotated around the y axis? c. Cross sections taken perpendicular to the y-axis are semicircles with diameter in region R. What is the volume of the solid?

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Please be mindful about each part! Include a sketch for each part to track your work. Thank you so much!!

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Step 1: Evaluation of (a) area and (b) volume

Step 2: Evaluation of (c) volume of slid

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