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Math22lO Quiz 9 (Section 13.1, 13.2, 13.3) Name Summer, 2012 Date Dylan Zwick 7-o/ Instructions: Ple’se show all of your work as partial credit will be given where appropriate, and there may be no credit given for problems where there is no work shown. All answers should be completely simplified, unless otherwise stated. 1. (15 points) Take the region R((x,y):0x4,0y8) ,the function +2xy—y+x and the partition P of R into eight equal squares by the 2 f(x,y)=x 3 linesx=2, y=2,y=4,andy=6. , Approximate iT f(x,y) f(Y) Ak , by calculating the corresponding Riemann sum assuming that (k,Yk) are the centers of the eight squares. 3 K L Answer: 2. Evaluate the following integrals. (J,i) ( /5) 5 (7/7) 77 I ) (a) ff(x2+x+y2+1)dxdy .(lOpoints) f’+ c3 31 f+ (+ - *YLtI) — ]dy I)+yj= f1yLJy *Lyt?Qy (3) yty3I ) Answer: 2 1 2—x (b) ff (x+y)dydx (15 points) —1 —x J(z -(x y1) UI 1 L i’1 5 IO ldJ 16 S Answer: )Jc iI x L 5 tj( vey - 7- j - + 75- - z_ Id