Math 224 Test 1 Fall Quarter 2011 Page 2 of 8
Question 1. Let x) be an even continuous function, and Jet be an odd continuous function.
Suppose that
8 8
f d3." : 9 and / 9(32) d2: : 13.
0 0
Compute the following integrals:
(a) (5 points) /08(3f(:v) + 2901
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Math 224-1 Midterm
Fall Quarter 2013
Tuesday, October 22, 2013
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Math 224 Exam 1
Winter Quarter 2013
February 6, 2013
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1:00
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Prob.
Poin
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Math 224
Midterm 2
March 3, 2015
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Math 224 Midterm I
February 3, 2015
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Math 224 Midterm 2 AM bo9 r k at]
March 3, 2015
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Math 224: Exam # 1
October 21, 2014
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Math 224 Worksheet #6, Winter 2015
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Final Exam
March 16, 2015
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Math 224: Exam # 1
October 21, 2014
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Math 224: Exam # 1
May 1, 2014
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Math 224
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Math 224 Midterm 2
Fall Quarter 2013
Tuesday, November 19, 2013
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Calegari 10:00 -
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Tamarkin
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Math 224 Final Exam
Fall Quarter 2013
December 11, 2013
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1
15
2
12
3
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Math 224 Final Exam
Winter Quarter 2013
March 18, 2013
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Belt
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1
12
2
16
3
8
4
6
5
10
6
26
7
14
8
12
9
12
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Math 224 Exam 1
Winter Quarter 2011
January 24, 2011
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Walker
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Khorami 11:00
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P
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Math 224 Exam 1
Winter Quarter 2010
February 1, 2010
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Treumann
Heller
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12:00
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1
10
2
6
3
4
4
12
5
40
6
15
7
3
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Math 224, Final Exam
Winter Quarter 2009
Question 1. (4 points) Suppose f (x) is an increasing function on the interval [2, 6].
6
f (x) dx using a left-endpoint approximation with n = 4, will your
If you
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Math 224 Exam 1
Winter Quarter 2013
February 6, 2013
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Score
0 Read each problem car
,.
l
.\ I
: w ,' - [7 ~ fl
L L/ l
/
Math 224 Worksheet #6, Winter 2015
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Test II, Math 224, Review Problems
1. Let R be the region bounded by the curves y = 7x, y = 14x and x = 1. Find
the volume of the solid obtained by rotating the region R about the x-axis.
2. Let R be the region bounded by the curve 4y = x2 , and x = 2y 4.
1
2.
dx
x + e2x
1
dx
= lim
e2x T
T
e2x dx =
1
1
.
2e2
1/2
1
Solutions to Test 2II Review Problems 49
2
2
(14x) (7x) dx +
V =
1.
49 (7x) dx =
3
0
1/2
We use washers to compute the volume and integrate along x from 0 to 1.
.
Here
is the picture The washe
Question 1 For each of the following questions, circle the correct answer. No explanation is necessary. No
partial credit will be given.
1. (3 points) Mich of the following integrals represents the length of the curve y = 1 + sin x from the
point (0,1) to
Math 224, SOLUTIONS OF THE REVIEW PROBLEMS FOR THE FIRST MIDTERM
Problem 1. Graphically, a denite integral is equal to the dierence of areas between
the graph and the x-axis, i.e. =(Area above Area below) the x-axis. Therefore, we
can compute these integr
Math 224 Worksheet #1, Winter 2015
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Math 224 Midterm 2
Fall Quarter 2016
Nov 14, 2016
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Math 224 Final Exam
Fall Quarter 2016
Dec 7, 2016
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Math 224 Midterm 1 - PRACTICE
Winter Quarter 2017
January 31st, 2017
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Math 224: Integral Calculus
Winter 2016 Final Exam
Instructions:
Roy-Fortin 8:00 am
Roy-Fortin 9:00 am
Sweet
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Jin
11:00 pm
Jin
12:00 pm
Cuzzocreo 1:00 pm
Maltenfort 2:00 pm
n
X
i=1
n
X
i=
n(n + 1)
2
n(n + 1)(2n
Math 224 Final Exam
Fall Quarter 2016
Dec 7, 2016
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