cheatham (sc36975) – HW01 – um – (53890)1Thisprint-outshouldhave17questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0 pointsEvaluate the integralI=913√x(√x+ 2)2dx .1.I=8152.I=353.I=234.I=45correct5.I=1115Explanation:Setu2=x. Then 2u du=dx, whilex= 1=⇒u= 1x= 9=⇒u= 3.In this case,I= 6311(u+ 2)2du= 6−1u+ 231.ThusI=−615−13=45.00210.0 pointsThe graph offhas slopedfdx=x2x2+ 1and passes through the point (2,3). Find they-intercept of this graph.1.y-intercept =−22.y-intercept =−533.y-intercept =−834.y-intercept =−735.y-intercept =−43correctExplanation:The functionfsatisfies the equationsf(x) =x2x2+ 1dx,f(2) = 3.To evaluate the integral setu= 2x2+ 1. Forthendu= 4x dx, in which casef(x) =14u1/2du=16u3/2+C=16(2x2+ 1)3/2+C ,whereChas to be chosen so thatf(2) = 3,i.e.,C+92= 3.Thusf(x) =16(2x2+ 1)3/2−27+ 3.Consequently, the graph hasy-intercept =−43.00310.0 pointsEvaluate the integralI=ln 20ex√4ex+ 1dx .1.I=123−√5correct2.I=343 +√5