CHAPTER 6 Applications of Integration
and the volume is
EXAMPLE 9 A wedge is cut out of a circular cylinder of radius 4 by two planes. One
plane is perpendicular to the axis of the cylinder. The other intersects the rst at an
angle of 30 along a diameter
193 Homework 1
Evaluate the integrals.
1.
(sin x 2 sec
2.
e
4x
2
x)dx
dx
3.
cos 2 xdx
4.
sec x(sec x tan x)dx
5.
1
3
2 1 x 2 1 x 2 dx
6.
sin x
x
7.
dx
3x
4x 2 5
8.
dx
1
x ln xdx
9.
sin
10.
x
2
5
1
dx
4
11.
csc
12.
2 x cos 2 xdx
2
(sin x ) cos xdx
x 2 1
Random Variables (section 5.2)
Given the followin A-robabili distribution:
III-"II '
(a) Find the probability thatX equals 2
P(X = 2) =
(b) Find the probability thatX is at least 1 (one or more )
P(X 21) =
(c) Find the probability thatX is at most 1 (on
The Multi lication Rule and Con itional Probabili section 4.5 _
When asked What is your political afliation, a large sample of DVC students gave the following results:
MM,
(Express all answers in 2 ways: as a fraction, and as a decimal rounded off to 3 si
434 CHAPTER 6 Applications of Integration
FIGURE 16
6.1 EXERCISES
1-4 Find the area of the shaded region.
We must integrate between the appropriate yvalues, y = 2 and y = 4. Thus
4 4
A = L (xx ' xL) dy = L [(y + 1) (a: 3)] dy
= I: (iyz + y + 4)dy
MATH 142
[1]
[2]
[3]
[4]
EXAM 2 TOPICS
Ch 4, 5
Vocabulary: experiment, sample space, event, etc.
n(A)
Theoretical probability: P(A) =
(no data is collected)
n(S)
f
Empirical probability; P(A) = relative frequency =
(data is collected)
n
(Disjoint) Events
Basic Probability (section 4.21 .
A bag contains marbles of the following colors: 126 green, 17 yellow, 1 black, and 7 red.
One marble is selected at random. Find the following probabilities.
Express your answers in 2 ways: as a fraction, and as a decimal
Math 294 Fall 2015 Quiz 3 Show all work So LK
5. A tank contains 400 liters of water in which 200 grams of salt is dissolved. A brine solution containing 8
grams of salt per liter of water is pumped into the tank at the rate of5 liters per minute, and the
3. PERSONAL STATEMENT
a.) I believe an exception should be made in my case because I have sincerely tried and proven that I can
pass college level classes with an appropriate comprehensive aide that is qualified, educated and
experienced in autism. DVC do
MATH 195 Practice Test 1 Solutions
Q1. P = If this year is a leap year then next year is not a leap year.
Q = This year is a leap year.
R = Next year is not a leap year.
P = Q -> R
a) Converse: R -> Q: If next year is not a leap year, then this year is a
Sam Ludden
Math 142
Professor Willett
5/18/13
Project #3
My project will be on the debating whether pre-workouts such as C4, which
have high doses of caffeine, actually boost your adrenaline levels during your
workouts at the gym for example. Pre-workouts
Math 142
Exam-4 Review
_
Section 8.3
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, an
Complement of at least 1= None
P(1)=
1P
Prob. Dist. =[x*P(x)]
2= [ ( x )2P ( x ) ]
P( AB)/ P( A)
Cond. Prob: P(B|A)=
Permutations Rule(items different): 1. n different items. 2.
We select r of the n items (without replacement).
nPr=n ! / ( nr ) !
or
[ x
Math 142
Review for Exam 3
_
Section 6.2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
Essential Questions
Math 192
3
5
1. Show that the equation 1 x 2x 3x 0 has exactly 1 real root.
_
2
2. Research the function and build the graph y x ln x. On the same graph draw
y x2 and compare their behavior.
_
3. Find the point on the line 3x 4y 12 , c
EssentialQuestions
Math192
1.FindthenumbercthatsatisfiestheconclusionoftheMeanValueTheorem.
f(x)=5x2+3x+6
x[1,1]
_
2.Evaluatethelimit:a)
;b)
_
3.Sketchthecurve.y=x/(x2+4)
_
4. Find the area of the largest rectangle that can be inscribed in a right triangl
/ Programmer: Yi Xu
/ Programmer's ID: 1440407
#include <iostream>
using namespace std;
int getResult(int, int);
int main()
cfw_
cout < "What's the result of one plus one?" < endl;
cout < "That's a such easy question! Result is: " < getResult(1,1) < endl;
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