Unformatted text preview: Tufts University -
Math 12 Department of Mathematics September 23, 2002
Exam 1 ’ 11:50-1:20 pm No calculators, notes or books allowed. You must show your work in the blue book and
cross out any work you do not want graded. Remember to sign your blue book. With your signature you are pledging that you have neither given nor received assistance on this
exam. 1. (15 points) a) Graph and shade the region bounded by the curves y— — 51:2 ,y = 2 + x,
' and y: 0.
b) Set up an integral(s) with respect to (ix that expresses the area of the region in
part a). Do not use absolute values. Do not compute the integral.
0) Set up an integral(s) with respect to dy that expresses the area of the region in
part a). Do not use absolute values. Do not compute the integral. 2. (15 points)
a) Evaluate fir/2 sin5 x dx. b) Write an integral(s) that gives the area between the curve y 2: sin5 a: and.the
x-axis for —7r / 2 S a: 3 7r. Do not evaluate it. 3. (10 points) Write out the form of the partial fraction decomposition of the following
rational function. DO NOT compute the constants. x4-7x+3 T“) = m Evaluate each integral listed below. (10 pts each) 7r 1r/6
4) f :1: sin 41: da: 6) / sin2 :1: cos2 :1: da:
5)./Vx2+9 d2: 7)/ 1——0—_‘”6;2+68dx 8)/(lna:)2dm 9”de ...
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