Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Welcome to Math 101Section 202!
Integral Calculus with Applications to Physical
Sciences and Engineering
Information about this course
Area problem
Courseinformation
My name: Hexi Ye. Email: [email protected]!
Website of the course: http:/www.math.ubc.
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Feb. 1, 2007
Marks
[2]
Math 101/206 Quiz 3
Dr. Haussmann
No aids allowed
Time: 15 min.
1. Sketch the region bounded on the left by the parabola x = y 2 and on the right by the
parabola x = 3 2y 2 , then nd its area.
1
0.5
0
0.5
1
1.5
x
2
2.5
3
0
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Mar. 1, 2007
Marks
[2]
Math 101/206 Quiz 5
Dr. Haussmann
No aids allowed
x2 4
1. Compute
dx. Hint: tan2 + 1 = sec2 .
x
Let x = 2 sec so x2 4 = 4(sec2 1) = 4 tan2 . Then
x2 4
2 tan
dx =
2 sec tan d
x
2 sec
=
Time: 15 min.
2 tan2 d
= 2 (sec2 1)
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Jan. 18, 2007
Marks
[3]
Math 101/206 Quiz 1
Dr. Haussmann
No aids allowed
Time: 15 min.
1. If
n
lim
n
2
2i
5+
n
i=1 n
10
b
=
f (x) dx
a
nd a, b, f .
It looks like we should take f (x) = x10 and xi = 5 +
2
and x = n = ba , hence b = 5 + 2 or b =
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS March 8, 2007
Marks
[2]
Math 101/206 Quiz 6
Dr. Haussmann
No aids allowed
Time: 15 min.
1
2
1. Use Simpsons rule with n = 4 to approximate
0
sum of ve fractions.
1
1
h = ( 2 0)/4 = 8 , y0 =
1
,
10
y1 =
1
1 1
8
dx
. Leave your answer as a
1x
, y2
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS March 15, 2007
Marks
Math 101/206 Quiz 7
Dr. Haussmann
No aids allowed
Time: 15 min.
[2]
dx
converges or diverges.
x2 + ln x
1
N.b. You will be unable to nd an antiderivative of the integrand.
1. Determine if
For x 1, ln x 0 so x2 + ln x x2 > 0.
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Feb. 15, 2007
Marks
[2]
Math 101/206 Quiz 4
Dr. Haussmann
No aids allowed
Time: 20 min.
1. Evaluate
t e3t dt.
(a)
Set u = t, dv = e3t dt to obtain
t e3t dt = t
(b)
e3t
3
e3t e3t
e3t
dt = t
+c.
3
3
9
e2t cos (t) dt.
0
Set u = e2t and dv = cos(t)
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS April 5, 2007
Marks
[2]
Math 101/206 Quiz 9
No aids allowed
Dr. Haussmann
Time: 15 min.
1. A tank contains 1000 L of water with 10 kg of salt dissolved in it. Pure water enters
the tank at a rate of 15 L/min and the solution drains out at the ra
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS March 22, 2007
Marks
[2]
Math 101/206 Quiz 8
Dr. Haussmann
No aids allowed
Time: 15 min.
1. A trough is lled with water (density =1000 kg/m3 ).The ends of the trough are
equilateral triangles with sides of length 2m and vertex at the bottom. Fin
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
SOLUTIONS Jan. 25, 2007
Marks
[2]
Math 101/206 Quiz 2
Dr. Haussmann
No aids allowed
Time: 15 min.
1. Evaluate
1
x
(a)
+
1
x3
dx.
1
x
(b)
1
1
+
1
x3
1
dx = ln x + x3 dx = ln x 2 x2 + c
x cos x dx.
1
1
x cos x dx = 0 since (x) cos (x) = x cos x so the i
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
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Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
MATHEMATICS 101 Section 201
Midterm #1
February 10, 2006
Calculators are not allowed.
Show all your work. Use backs of pages if necessary.
Check to ensure that this exam has 4 pages.
This exam is out of 40 marks.
Name:
Student ID:
Class ID:
1. (12 marks)
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
MATHEMATICS 101 Section 201
Midterm #1
February 10, 2006
Calculators are not allowed.
Show all your work. Use backs of pages if necessary.
Check to ensure that this exam has 4 pages.
This exam is out of 40 marks.
Name:
Student ID:
Class ID:
1. (12 marks)
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Full Solutions
MATH101 April 2013
December 4, 2014
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Full Solutions
MATH101 April 2007
April 16, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite re
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Full Solutions
MATH101 April 2010
April 16, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite re
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Full Solutions
MATH101 April 2013
April 16, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite re
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Full Solutions
MATH101 April 2011
April 16, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite re
Integral Calculus with Applications to Physical Sciences and Engineering
MATH 101

Spring 2007
Full Solutions
MATH101 April 2008
April 16, 2015
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. This document
provides full solutions that you can use to grade your work.
If youre not quite re