MATH 2263 Midterm: MATH 2263 UMN Exam 2 Solutions
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October 30, 2008: (10 points) let r be the rectangle 2 x 2, 0 y 1. Find the double integral rrr x2 y+1 da. 3(y+1)i2 x2 y+1 da = r 1 y=0r 2. 3 h ln(y + 1)i1 dy = 16 x= 2 y=0 x2 y+1 dx dy = 3 ln 2: (10 points) let r be the rectangle 0 x 5, 0 y 2 in the (x, y)-plane. If a continuous function f (x, y) satis es 1 f (x, y) 3 y2, what does this tell you about the value of. Solution: since 1 f (x, y) 3 y2, the only information we have is that. So since rrr 3 y2 da = r 2 this only tells us that ( 1) da zzr. 2r 5 f (x, y) da zzr. 0 (3 y2) dx dy = 5h3y y3. 10 zzr f (x, y) da .
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