Answer:
[tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
Integrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {x \ln x} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = \ln x[/tex][u] Logarithmic Differentiation: [tex]\displaystyle du = \frac{1}{x} \ dx[/tex]Set dv: [tex]\displaystyle dv = x \ dx[/tex][dv] Integration Rule [Reverse Power Rule]: [tex]\displaystyle v = \frac{x^2}{2}[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \int {\frac{x}{2}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \frac{1}{2} \int {x} \, dx[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \int {x} \, dx \bigg)[/tex][Integral] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \frac{x^2}{2} \bigg) + C[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Question 7(Multiple Choice Worth 5 points)
(04.02 MC)
The two-way frequency table contains data about students' preferred exercise.
Likes running 28
Does not like running 46
Column totals 74
What is the joint relative frequency of students who do not like to run and enjoy swimming?
O23%
37%
Enjoys swimming Enjoys cycling Row totals
62
90
64
110
126
200
46%
072%
The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.
Given the following information from the table:
Likes running: 28
Does not like running: 46
Column totals: 74
Enjoys swimming: 62
Enjoys cycling: 90
Row totals: 110
The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:
Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)
From the table, the number of students who do not like running and enjoy swimming is given as 46.
Total number of students is given as 74.
Joint relative frequency = 46 / 74
Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.
Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.
In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
To know more about Frequency .
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Suppose that when a system of linear equations is graphed, one line completely overlaps the other line. Which statement is correct?
The system of equations has one solution because the lines intersect at one point.
The system of equations has one solution because the lines do not intersect at only one point.
The system of equations does not have only one solution because the lines intersect at one point.
The system of equations does not have only one solution because the lines do not intersect at only one point.
Answer:
The system of equations does not have only one solution because the lines do not intersect at only one point.
Step-by-step explanation:
If the lines are covered by each other, they intersect at all the points they overlap on. So, there is more than on solution.
The following statement is correct.
The system of equations does not have only one solution because the lines do not intersect at only one point.
The following information should be considered:
In the case when the system of linear equations is graphed and one line is overlap to the other one.So here the system of equation contains more than one solution as the lines are not intersected at only one point but more than one point.Learn more: brainly.com/question/17429689
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
A pool measuring 12 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 576 square meters, what is the width of the path?
The width of the path is __?__ meters
Answer:
path width = 3 m
Step-by-step explanation:
let x = the width of the path
(12 + 2x)(26 + 2x) = 576
312 + 24x + 52x + 4x² = 576
4x² + 76x - 264 = 0
divide both sides of the equation by 4:
x² + 19x - 66 = 0
(x + 22)(x - 3)= 0
x = 3 m
What is the volume of a cylinder, in cubic cm, with a height of 8cm and a base
diameter of 18cm? Round to the nearest tenths place.
A rectangular prism has a height of 5 meters a length of 8 meters and a width is 9 meters. What is the volume of the prism
HELP PLSSSS
hey can u look at the pic above pls and help
Answer:
1,296 students attended the fall play.
Step-by-step explanation:
Let the amount of students = s
Let the amount of adults = a
Three times the adults: 3a
150 fewer than three times the adults:3a-150
amount of students = 150 fewer than three times the adults: s=3a-150
We also know that a+s=1778. Let's sub in the value for s that we got above:
a+s=1778
a+3a-150=1778
4a=1928
a=482
a+s=1778
482+s=1778
s=1296
Wendy is making potato salad for a picnic. One sack of potatoes weighs 14 pounds.What is the weight of a sack of potatoes in ounces
Answer:
224 ounces
Step-by-step explanation:
1 pound is 16 ounces, 14 multiplied by 16 is 224
every pound equal 16 ounces so 14 × 16 = 224
An angle equal to its supplement is _____ degree.
Answer:
90 Degrees.
The angle which is equal to its supplement is 90 degrees.
Answer:
90
Step-by-step explanation:
Let the required angle be x°
Therefore, it's supplement = (180-x)°
Now, x = 180-x
= x+x = 180
= 2x = 180°
Therefore x\ =\ \frac{180°}{2}\ =\ 90°x = 2180° = 90°
A company sells meal kits. Suppose that 70% of the first-time customers who order a vegetarian meal will order
again, while 65% of the first-time customers who order a gluten-free meal will order again. The company takes
separate random samples of 50 first-time customers who order each kind of meal. The company will then look at
the difference (vegetarian – gluten free) between the proportions of customers who order again in each
sample.
What will be the shape of the sampling distribution of the difference in sample proportions, and why?
Answer: A
Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10
Step-by-step explanation: Khan Answer
For vegetarian orders 70% order again, so with a sample size of 50 we will have an estimated 35 people order again: [tex].7*50=35,50-35=15[/tex] This results in 35 successes and 15 failures. For gluten-free orders 65% order again, so with a sample size of 50 we will have an estimated 32.5 people order again:[tex].65*50=32.5,50-32.5=17.5[/tex] This results in 32.5 successes and 15 failures. Because these are all greater than 10, we can assume normality.
Answer:
Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10
Step-by-step explanation:
A 2-gallon jug of juice costs $14.72. What is the price per cup?
Answer:
3we
Step-by-step explanation:
rffd
calculate (4-3,5(2 1/7-1 1/5)):0,14
Answer:
sin (330)
cos (390)
csc (60)
------------------------------------------------
Hope this helps!!! :)
Which product is greater than 63
Answer:
3/2 times 63
Step-by-step explanation: took quiz
Find the perimeter of a quadrilateral with vertices at C (-1, 2), D (-2, -1), E (2, -2), and F (1, 1). Round your answer to the nearest hundredth when necessary.
A. 10.92 units
B. 12.68 units
C. 13.43 units
D. 18.27 units
Answer:
B 12.68
Step-by-step explanation:
you will need to find the distance between each segment-
so the length of DC, CF, FE, ED
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]
DC:
D(-2,-1) C(-1,2)
[tex]d=\sqrt{(-1--2)^{2} +(2--1)^{2} } \\d=\sqrt{1^{2}+3^{2} } \\d=\sqrt{10} =3.16[/tex]
CF:
C(-1,2) F(1,1)
[tex]d=\sqrt{(1--1)^{2} +(1-2)^{2} } \\d=\sqrt{2^{2}+-1^{2} } \\d=\sqrt{4+1} \\d=\sqrt{x} 5=2.24[/tex]
FE
F(1,1) E(2,-2)
[tex]d=\sqrt{(2-1)^{2} +(-2-1)^{2} } \\d=\sqrt{1^{2} +(-3)^{2} } \\d=\sqrt{1+9} \\d=\sqrt{10}= 3.16[/tex]
ED
E(2,-2) D(-2,-1)
[tex]d=\sqrt{(-2-2)^{2} +(-1--2)^{2} } \\d=\sqrt{(-4)^{2}+1^{2} } \\d=\sqrt{16+1} \\d=\sqrt{17}= 4.12\\[/tex]
3.16+2.24+3.16+4.12= 12.68
If the two spinners below are spun, what is the probability that the numbers will add to less than six?
Answer:
3/4 or 75%
Step-by-step explanation:
There are twelve possible outcomes. (4 green for each of the three orange).
The only combinations that add up to six or more are 2&4, 3&3 and 3&4.
That’s 3 out of 12. So 9 out of 12 combinations will add up to less than 6.
9/12=3/4 or 75%
Answer:
3/4
Step-by-step explanation:
I need help with this yes or no picking?
Change 7 kilograms into grams.
Answer:
it's. 7000
Step-by-step explanation:
1 kg = 1000 g
7 kg × 1000 g = 7000g
Answer -. 7 kg = 7000 g
Thanks
The area of a circle is 4 square centimeters. What is the circumference?
Select the two figures that are similar to each other.
please help me thanks
Answer:
D
Step-by-step explanation:
Answer:
each person gets 2 1/2
Step-by-step explanation:
You divide and get 2 1/2
the answer is D
Without graphing, tell whether the line containing (6. -3) and (0, -8) is horizontal, vertical, or neither.
A neither
O B. vertical
ci horizontal
Suppose that the height (in centimeters) of a candle is a linear function and the amount of time (in hours) it has been burning. After 9 hours of buring, a candle has a hight of 22.2 centimeters. After 23 hours of burning, it's heigh is 16.8 centimeters. What is the height of candle after 19 hour
Answer: cockme
Step-by-step explanation:
cockme
Steve earns $6.50 an hour. He worked 25 hours in the previous 1-week pay period. If Steve's employer withholds 10% of each of Steve's paychecks to pay Steve's income tax, how much will Steve take home in this week's paycheck?
Answer:
$146.25
Step-by-step explanation:
$6.50 per hour
for 25 hours = 25 × 6.50 = $162.5
10% of 162.5
162.5 × 10 ÷ 100
= 16.25
his week paycheck
162.5 - 16.25
= $146.25
Answer:
146.25$ is the a answer for sure
help me .................
Answer:
The answer is 6 and 1/12 yards :]
C2>a2+b2 is it a obtuse right or acute
Answer:
obtuse
Step-by-step explanation:
When c, the hypotenuse, is greater than the legs (a and b), it's an obtuse triangle
if 3 inches represents 65 miles on a map, then how many inches represent 195 miles?
Answer:
Step-by-step explanation:
65 miles = 2 inches
65 * 3 miles = 2 * 3 inches
195 miles = 6 inches
You roll a fair die three times. What is the probability of each of the following? a) You roll all 2's. b) You roll all odd numbers. c) None of your rolls gets a number divisible by 3. d) You roll at least one 4. e) The numbers you roll are not all 4's.
Answer:
[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex][tex]=\frac{1}{72}[/tex]
[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2} =\frac{2}{8}[/tex]
[tex]\frac{4}{6}[/tex]×[tex]\frac{4}{6}[/tex]×[tex]\frac{4}{6} =[/tex][tex]\frac{8}{27}[/tex]
[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex][tex]=\frac{1}{72}[/tex]
[tex]\frac{8}{27}[/tex]
if the measure of arc LK is 56 degrees and the measure of arc LM is 187 degrees, what is m JKM angle KL = 56 degrees
Answer:
JKM is 123 degrees and the measure of arc KL is 56
3(v +67)=-13 I need help
Answer:
v= -71.3 there you go hope this helps
There are 12 boys and 15 girls in your class for new students three boys and one girl join your class what is the ratio of the class before the new students and after the new students arrived
Answer:
4/5 : 15/16
Step-by-step explanation:
Ok let's write the ratio of boys to girls before the new students arrived
12 : 15
Simplify :
12/3:15/3
4 : 5
Lets write the ratio of students after the new students arrived
15 : 16
Cannot be Simplified.
We have two ratios
Lets write them as fractions
4 : 5 = 4/5
15 : 16 = 15/16
The new ratio should be
4/5:15/16
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-Chetan K