2312FinalReview - Final Exam covers the material from lecture 1 through 23 and Lecture 36 through 39 This set of review problems are not meant to be

2312FinalReview - Final Exam covers the material from...

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Final Exam covers the material from lecture 1 through 23 and Lecture 36 through 39. This set of review problems are not meant to be comprehensive. 1. Use thediskmethod, find the volume of the solidgenerated by rotating the region bounded byy= (1 +x2)14and thex-axisfromx= 0 tox= 1 about thex-axis.2. Determine the most appropriate way to findthe volume of this solid generated by rotating the regionbounded byx= siny, x= 2 +y, y= 0andy=πabout the linex=-1. Set up the integral to calculate the volume.3. Use the Shell method, find the volume of the solid generated by rotating the region bounded byy=e-x2/2, y=-e-x2/2about they-axis.4. Find the volume of the solid generated by rotating the region bounded byy= cosxandy= cosxsinxfromx= 0 tox=π4, about thex-axis. (hint: cosxcosxsinx).5. Find the area of the region which lies between the curvesy= sin2(x) andy= cos2(x) for 0xπ. 1

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