MATH124 CALCULUS II for Engineers
Midterm 1
(50 pts)
Please print names and IDs in ink :
Course Section:
February 11, 2009
NSID:
Family Name:
First Name:
Student ID:
INSTRUCTIONS:
1. Time Limit: 80 minutes
2. No cheating.
3. Simplify all answers unless ot
MATH124 CALCULUS II for Engineers
Lab Section:
Solution Key for Midterm 2 (50 pts)
1. (4 pts) Find the area of the bounded region determined by the equations x = y(1y) and x = 3y(1y).
Take horizontal strips.
1
1
0
2
1
(3y 3y 2 y + y 2 ) dy = 2
[3y(1 y) y(
MATH124 CALCULUS II for Engineers
Quiz 4
(12 pts)
February 11, 2015
Please print names and IDs in ink :
Family Name:
NSID:
First Name:
INSTRUCTIONS:
Lab Section: L
1. Time Limit: 30 minutes
2. No cheating.
5. Show all your work.
Student ID:
3. Closed book
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MATH124 CALCULUS II for Engineers
Lab Section: L
Solution Key for Quiz 8 (12 pts)
x2 x + 2
dx.
x4 + x2
1. (4 pts) Evaluate the indenite integral
x2 x + 2
x2 x + 2
Cx + D
A
B
= 2 2
= + 2+ 2
4 + x2
x
x (x + 1)
x
x
x +1
x2 x + 2 = Ax(x2 + 1) + B(x2 + 1) + x2
MATH124 CALCULUS II for Engineers
Solution Key for Quiz 3
(12 pts)
n
b
1. (4 pts) Use equation
Lab Section: L
f (x) dx =
f (x ) xi , to evaluate the denite integral
i
lim
xi 0
a
i=1
3
(x2 2x) dx. For each n = 1, 2, 3, . you are required:
1
(a) to choose a
MATH124 CALCULUS II for Engineers
Solution Key for Quiz 6
Lab Section: L
(12 pts)
1. (4 pts) Find the centroid of the region bounded by the curves y = x2 and y =
1
A=
0
2 x3
( x x2 ) dx = x3/2
3
3
1
Ax =
=
0
(x3/2 x3 ) dx = x2
0
Ay = Ax =
x.
2 1
1
=
3 3
MATH124 CALCULUS II for Engineers
Solution Key for Quiz 6
0
1. (4 pts) Determine whether the integral
Lab Section: L
(12 pts)
10x3
dx converges or diverges. If it converges nd
+ 5)6
(x4
its value.
0
10x3
dx = lim
a
+ 5)6
(x4
10x3
dx = 10
(x4 + 5)6
0
a
10x
MATH124 CALCULUS II for Engineers
Lab Section: L
Solution Key for Quiz 2 (12 pts)
1x
dx. Suggested substitution y = x.
x+x
1. (4 pts) Evaluate the indenite integral
If y =
x, then y 2 = x and 2y dy = dx.
1x
dx =
x+x
1 y2
2 y dy = 2
y(1 + y)
1 y2
2y dy =
MATH124 CALCULUS II for Engineers
Lab Section: L
Solution Key for Quiz 5 (12 pts)
1. (4 pts) If the force of a crossbow (in Newtons) is proportional to the draw (in metres), i.e. F = kx,
and it is 240 N at a full draw of 40 cm, what work is required to fu
MATH124 CALCULUS II for Engineers
Lab Section: L
Solution Key for Quiz 1 (12 pts)
1. (4 pts) Under adiabatic expansion, a gas obeys the law P V 7/5 = a constant, where P is the pressure
and V is volume. If the pressure is increased by 7%, nd the approxima
MATH124 CALCULUS II for Engineers
Lab Section:
Solution Key for Midterm 1 (50 pts)
Part 1. Handwritten Answers.
Write down the solution to the following problem, giving all necessary details, in the space
provided.
n
b
f (x) dx =
1. (a) Use equation
xi 0
MATH124 CALCULUS II for Engineers
Lab Section:
Solution Key for Midterm 2 (50 pts)
Part 1. Handwritten Answers.
Write down the solution to the following problem, giving all necessary details, in the space
provided.
1. (a) For f (x) = x2 /2, where x [0, 1]
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MATH124.3 CALCULUS I1
2006-2007
M idterm 1 (40
1
Please p rint names a nd IDS in ink:
Family N ame:
INSTRUCTIONS:
1 . T ime Limit: 80 minutes
2 . No cheating.
3 . W rite clearly & legibly.
February 7, 2007
p ts)
1 First Name:
S tudent ID:
4. Closed book.