Math 172FINAL EXAMSpring 2014Name:ID#:Lab section:SHOW APPROPRIATE WORK or EXPLANATION on each problem for full credit. Box or circle your finalanswers. Calculators/note sheets are NOT allowed. Numbers in the [ ] indicate what each problem is worth. Helpsheet is the last page of the exam, which you may detatch if you like.1. DefineAto be the region in the first quadrant below the curvey= 2 and between the curvesy=12x2andy= 2x. Sketch regionAas best you can, and then use definite integral(s) to find its area.2.[6 each] Define regionBto be the region shown on the right, which isbounded by the curvesy=x2andy= 9.
b) Set up, but do not evaluate, definite integral(s) for finding thevolume of the solid formed whenBis rotated about the linex= 4.