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 whethereach 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)integraldisplay∞31x2√x2-9dxType: 1 , 2You may use thatintegraltext1x2√x2-9dx=√x2-99x+C(c)integraldisplay∞0e-x(1-x)dxType: 1 , 2Hint: integrate by parts.
2. Use the comparison test for improper integrals to show thatintegraldisplay1exxdxdiverges.03. Consider the region bounded by the curvesy=+√1-x2andy=|3x| -3.(a) Sketch the enclosed region.