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Unformatted text preview: Math 168
Kouba
Exam 2 Print your name here. Your exam ID # 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. No notes, books, or classmates may be used as resources for this exam.
It is a violation of the University honor code to, in any way, assist another
person in the completion of this exam. Please keep your own work covered
up as much as possible during the exam so that others will not be tempted
or distracted. Thank you for your cooperation. 3. Read directions to each problem carefully. Show all work for full
credit. In most cases, a correct answer with no supporting work will not receive full credit. The best way to get maximum partial credit is to
write neatly and be organized. V 4. Make sure that you have seven (7) pages, including the cover page. 5. Include units on answers where units are appropriate. 6. YOU WILLBE GRADED ON PROPER USE OF integral (l), dx, du, and dv
notation. 7. You have until 8:50 am. to complete the exam. page 2 of 7
1.) (6 pts. each) Integrate. 3.
a.) J(x+1)ex +2x'5 dx b.) Ix(1_x)20 dx 0.) I sec‘ox tanx dx ms x3+1o dx
x+3 e.) Jinx dx 4 m Ila2xdx
0 g) I(1+sm3x)2dx h.) Ix  cosx dx i.) Jezx J3+ex dx page 3 of 7 page 4 of 7
2.) (4 pts.) Estimate the value of the following definite integral by computing M 3, the
Midpoint Rule estimate with n = 3. Write your answer as a decimal to three decimal places. 6
I44+x2 dx
0 3.) (6 pts.) Find the area of the region bounded by the graphs of A 4~ and 7‘ . SET
UP BUT DO NOT EVALUATE THE INTEGRAL(S)4 x: 37 :L K : q,Y a, 4.) (8 pts.) Find the area of the region bounded by the graphs of y = sin x and y = sin 2x on
the interval [0, 21:]. SET UP BUT DO NOT EVALUATE THE lNTEGRAL(S). page 5 of 7 5.) (6 pts.) The velocity of a car at time t hours is given by v(t) = 50 t e"t 2 mph. How far
does the car travel between t = 0 hrs. and t = 2 hrs. ? Write your answer as a decimal to one decimal place. 50
6.) The outdoor temperature (0F) at time t hours is given by T = 40 + (1+ 1)2 0 a.) (2 pts.) What is the initial temperature ? What is the temperature after t = 4 hours ? b.) (2 pts.) At what rate is the temperature changing when t = 4 hrs. 7 c.) (4 pts.) What is the average temperature between t = 0 and t = 4 hours ? page 6 of 7 7.) (‘7 pts, each) Consider the region bounded by the graphs of y = e x , x = In 5. y = O , and
x = 0. SET UP BUT DO NOT EVALUATE THE INTEGRAL(S) which represent the volume of the
solid formed by revolving this region a.) about the xaxis. b.) about the yaxis. paage 7 of 7
EXTRA CREDIT PROBLEMS Each of the following problems is worth 8 extra credit points.
These problems are optional. 1.) Integrate SJI + F dx 3 :L
2.) Assume that y = f(x) is an odd function and that I f(x) dx = 7 and J f(X) dx = 4 .
3 I 'l
Find the value of I f(x) dx.
2 ...
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 Spring '10
 Kouba
 Calculus, pts, Decimal, dx

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