DGQ08-solutions - Version 055 DGQ08 gilbert(54820 This...

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Version 055 – DGQ08 – gilbert – (54820)1Thisprint-outshouldhave4questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0pointsEvaluate the triple integralI=integraldisplay20integraldisplayy0integraldisplayx0(2z+y)dzdxdy .1.I=103correct2.I=833.I= 44.I=1135.I= 3Explanation:As a repeated integral,I=integraldisplay20parenleftBigintegraldisplayy0parenleftBigintegraldisplayx0(2z+y)dzparenrightBigdxparenrightBigdy .Nowintegraldisplayx0(2z+y)dz=bracketleftBigz2+yzbracketrightBigx0=x2+xy ,whileintegraldisplayy0(x2+xy)dx=bracketleftBig13x3+12yx2bracketrightBigy0=56y3.Consequently,I=integraldisplay2056y3dy=103.keywords:integral,tripleintegral,re-peated integral,linear function,polynomialintegrand, binomial integrand,evaluation oftriple integral
00210.0pointsA cylindrical drill with radius 4 inches isused to bore a hole through the center of asphere of radius 5 inches to produce a solid

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