Solved Exam for Multivariable Calculus | MATH 2224, Exams of Calculus

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oboe Math 2224 Test 2 Fall 2010 Name rin You may not use any notes, text, other people or their work, or electronic devices. Must show work on problems other than multiple choice or matching. Use proper units. . 1 Given fz,y)=x’y and the region D in the xy plane bounded by y = x- 2 and y =- x. a.( 8 pts) Sketch the region D and set up the double integral for the area D as simple in x. u l ~* . % “2 F-¥ xe ex 2 =O Ae Jt fo dydx J (eater) =° * xe-t vel Md b, (7 pts)Set up the double integrals for the moment about y, M,, for the center of mass of the region in part “a” if the density function is 6(x,y)}=s, where k is a constant. nyt \ 4 ff Kx dydx Royet c. (6 pts) Set up the double integral for volume for the solid bounded above by. ‘S{G.y)=x’y and below by D. 1 -x* / Ve § J xy dyax -toge d.(8 pts} Set up the volume in part “c” as a triple integral. boext oxy V = S S J besyse -@ Kt My = v\ Tay 4 * 2. (16 pts.) Integrate: f i [ay?dsdyde = ot f zy? x i, lyda “ee a20 Leave answer in as two fractions. * 2 1 27 | 2 (Dp 2° 2 2 d an oS eye JS ie de = Jd =< 5 & Lf >) > -a Over. | 5 2 a =O um eo A