calc 2 fianl exam old a.pdf - Math 172 Name FINAL EXAM ID...

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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.[10] 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.
3.[10 each] Integrate.a)integraldisplay31ln(x)x2dxb)integraldisplay2x+ 1x2-2x-15dx
4.[10 each] Integrate.a)integraldisplay21(2x-3)3/2dxb)integraldisplayx2-9x3dx(use a trig. sub.)

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