# Quiz 7 2014 Answers - Arts & Science 1D06 Quiz #7 29...

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Arts & Science 1D06 Quiz #729 January 2015 1:30 pmFull Name:Student # :TA:Please provide detailed solutions to the problems below. Correct responses without justification may notreceive full credit. The use of a calculator is permitted.1. Determine the type of each of the following improper integrals (circle your choice(s)) and whether[6]each is divergent or convergent.Evaluate those that are convergent.Hint:Type 1 improperintegrals have an infinite interval and Type 2 improper integrals have discontinuous integrands.(a)integraldisplay40xx2-4dxType: 1 , 2(b)integraldisplay31x2x2-9dxType: 1 , 2You may use thatintegraltext1x2x2-9dx=x2-99x+C(c)integraldisplay0e-x(1-x)dxType: 1 , 2Hint: integrate by parts.
2. Use the comparison test for improper integrals to show thatintegraldisplay10exxdxdiverges.[2]3. Consider the region bounded by the curvesy=+1-x2andy=|3x| -3.[4](a) Sketch the enclosed region.xy-4-3-

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