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
Plzzzzzz helppppp meeee !!!
ABC is similar to FED. Answer the questions to find the length of DF.
1. Which side in AFED does AB in AABC correspond to?
2. Which side of FED does CB in ABC correspond to?
3. Which side of FED does AC in the ABC correspond to?
4. What scale factor was used in the dilation of ABC to FED? Explain how you found the scale factor.
5. What is the length of side DE? Show how you found the length.
6. Use the Pythagorean theorem to find the length of side FD. Show your work.
Answer:
Corresponding side of AB is FE
Corresponding side of CB is DE
Corresponding side of AC is FD
[tex]k =2[/tex]
[tex]DE = 6[/tex]
[tex]FD=10[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABC[/tex] and [tex]\triangle FED[/tex]
See attachment for triangles
Solving (a): Corresponding side of AB
Going by the names of the triangle, the corresponding sides are:
AB and FE; CB and DE; AC and FD
Hence, the corresponding side of AB is FE
Solving (b): Corresponding side of CB
This has been solved in (a) above.
The corresponding side of CB is DE
Solving (c): Corresponding side of AC
This has been solved in (a) above.
The corresponding side of AC is FD
Solving (d): Scale factor from ABC to FED
To do this, we simply divide the lengths of corresponding sides.
The scale factor k is:
[tex]k = \frac{FE}{AB}[/tex]
[tex]k = \frac{8}{4}[/tex]
[tex]k =2[/tex]
Solving (e): Length of DE
We make use of the scale factor calculated in (d) above
[tex]k = \frac{DE}{CB}[/tex]
[tex]2 = \frac{DE}{3}[/tex]
[tex]DE = 2 * 3\\[/tex]
[tex]DE = 6[/tex]
Solving (f): Length of FD
Using Pythagoras:
[tex]FD^2 = DE^2 + EF^2[/tex]
[tex]FD^2 = 6^2 + 8^2[/tex]
[tex]FD^2 = 100[/tex]
[tex]FD = \sqrt{100[/tex]
[tex]FD=10[/tex]
What is the value of 3x + 5y, when x = 12 and y = 4? 24 А B В 48 C 56 D 72
Answer:
C is the answer
Step-by-step explanation:
All you have to do is plug 12 in for x and 4 in for y
3(12) + 5(4) = solve
36 + 20 = 56
Hope that helps
The area of Region A is the same as the area of region c true or false
Answer:
True
Step-by-step explanation:
Problem is in picture
Answer:
< ABC+<QRS=180
m<QRS=180-140=40°
Answer:
Solution given:
<ABC+<QRS=180° {supplementary]
m<QRS=180°-140°=40° is your answer
What is the description of the translation from f(x)=9x+3 to g(x)=4x+3?
Answers:
A. Moved Up
B: Counterclockwise Rotation
C: Clockwise Rotation
D: Moved Down
Answer:
Clockwise rotation
Step-by-step explanation:
Took the test, the other answer here was incorrect
HELP DUE IN 2 MINUTESS!!!! PLS HELP
An Urn contains 6 red marbles and 9 white marbles. A marble is drawn and put back into the urn. Both marbles were red. If another marble is drawn, what is the probability of it being white?
Answer:
3/5
Step-by-step explanation:
favorable outcomes/total number of outcomes=probability
Answer:
[tex] \frac{3}{5} [/tex]
Step-by-step explanation:
Previous extractions do not influence the probability
Hey can someone help me measure these angles
Answer:
A is acute and B is obtuse.
Step-by-step explanation:
This is because any angle less then 90 is acute and any angle over 90 degreee is obtuse.
Given P(A) = 0.4, P(B) = 0.58 and P(A|B) = 0.5, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
By definition of conditional probability,
P(A | B) = P(A and B) / P(B)
so
P(A and B) = P(A | B) P(B) = 0.5 × 0.58 = 0.29
A file that is 263 megabytes is being downloaded. If the download is 17.6% complete how many megabytes have been downloaded?
Answer:
46.288 megabytes
Step-by-step explanation:
megabytes that have been downloaded
= 17.6% of 263
[tex] = 0.176 \times 263 \\ = 46.288[/tex]
Solve for mZIJL.
K
\100°
52°
o
Answer: mZIJL
Submit Answer
Answer:
m<IJL = 48
Step-by-step explanation:
<IJL = x
100 - 52 = x
x = 48
Which of the following are not parts of a pyramid? diameter, altitude, radius, lateral edges, vertex.
Answer:
Radius and diameter are not part of a pyramid
10th grade geometry question. I will give brainliest. NEED HELP ASAP
Answer:
(-4+5)-1
Step-by-step explanation:
Help pls fast ....................
Answer:
its A. 5
Step-by-step explanation:
5/10 is also known as 1/2 so 5/10 is equal to 1/2
somebody please help this is due in a couple of hours :(
Answer:
Step-by-step explanation:
Solve for x.
3x + 7 = 28
O A. x=-7
OB. x= 2.3
O c. x=7
OD. = 11.6
E. x = 18
Answer:
The answer is C, x = 7.
Step-by-step explanation:
3x + 7 = 28
-7. -7
3x = 21
/3. /3
x = 7
cesium-137 has a half-life of approximately 30 years. how much of a 40g sample would be left after 90 years?
Answer:
5g
Step-by-step explanation:
the first half life would be 20 the next, 10. and lastly 5
Help me please with my IXL GEOMETRY
Answer:
7.5
Step-by-step explanation:
hey hope this helps and is right
What is the slope of the line 3y = 4x + 5?
Answer:
4/3
Step-by-step explanation:
Simplify the expression $(x-4)(x-7) + (3-x)(2+x).$
Help please! make sure to remember you have to simplify! not solve!
sese
Sam has a phone card that charges $1 to connect and $0 50 per minute. He also uses a cell phone that charges $3 to connect and $0.25 per
minute. In how many minutes will calls made using the phone card and the cell phone cost the same?
Answer:
8
Step-by-step explanation:
Jen needs to save $180 for a new camping tent. She is able to save $9 each week. How many weeks will Jen need to save to reach her goal? Write an equation to solve the problem. Explain how you found your answer.
Answer:
i got 20 weeks. i divided 180 by 9 and i got 20. i'm not sure if it's what you're looking for, but i hope it helps.
Step-by-step explanation:
Running at an average rate of 10 m/s, a sprinter ran to the end of a track and then jogged back to the starting point at an average of 5 m/s. The sprinter took 60 s to run to the end of the track and jog back. Find the length of the track.
d=300md is equal to 300 m
d=200md is equal to 200 m
d=600md is equal to 600 m
d=150md is equal to 150 m
9514 1404 393
Answer:
200 m
Step-by-step explanation:
Let d represent the length of the track in meters. The relation of interest is ...
time = distance/speed
Then the total time to run and walk back is ...
60 = d/10 + d/5
600 = d + 2d
200 = d . . . . . . . divide by 3
The length of the track is 200 meters.
_____
200 m in 20 seconds is a world-record time for a woman; a very good time for a man.
BRAINLIEST FOR CORRECT ANSWER, IM FAILING SCHOOL AND NEED HELP ASAP. EVEN OFFICIAL HELP COUNTS
Answer:
1. Supplementary angles
2. alternate exterior
3. verticle angles
4. alternate interior
The box matches the numbers. 1 is the answer in the first box, and so on.
Let me know if you have any questions
id really appreciate it if someone helped me , i’ll give you brainliest
Answer: it’s the same 110 degrees
Step-by-step explanation:
Answer: 110 is the correct answer
when do we say two points are said to be collinear
Answer:
never heard of that word lol
Step-by-step explanation:
May I have some help with this please?
f(x) = |7m + 4| = 1
First equation by taking positive modules
7m + 4 = 1
7m = -3
m = -3/7 . Ans.
Second equation by taking negative modules
-7m - 4 = 1
-7m = 5
m = -5/7 . Ans.
∴ m = [ -5/7 U -3/7 ] Ans .
Solve these equations. Show solutions on a number line.
|x-7|=x-7
Answer:
X is equal to or greater than 7
Step-by-step explanation:
Since lx-7l is equal to x-7, this means that it can only work on places where the lines are on top of each other. In terms of x, this means that x must be at least 7. As you can see in the number line also attached.
please help me with this
Answer: [tex]30^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\sin 60=\dfrac{\sqrt{3}}{2}[/tex]
For
[tex]\cos \theta =\dfrac{\sqrt{3}}{2}[/tex]
It indicates [tex]\theta[/tex] lies in I st quadrant. The value of cosine [tex]30^{\circ}[/tex] is equal to [tex]\dfrac{\sqrt{3}}{2}[/tex]
Therefore, [tex]\theta[/tex] must be [tex]30^{\circ}[/tex]
A tutor earns $220 for 4 hours of tutoring. At the same rate, how much would the tutor earn for 3 hours of tutoring?
A. $150
B. $155
C. $165
D. $180
You want to have $150,000 in your retirement account when you retire in 30 years. Your retirement account earns 7%
interest. How much do you need to deposit each month to meet your retirement goal?
Round your answer to the nearest cent.
Do NOT include the dollar sign.
Answer: 123.05
Use annuity formula
Answer:
Step-by-step explanation:
Since we're talking about making a deposit of a certain amount every month rather than just one big deposit, we are talking about an annuity. The formula for the value of an annuity is A(t)=d[(1+rn)nt−1](rn) where A(t) is the value of the annuity, d is the amount of each deposit, n is the number of deposits per year, t is the number of years, and r is the rate of interest. In this case we know we want the value of the annuity to be A(t)=$150,000, we want to make deposits every month, or 12 times a year, so n=12, we want to reach our desired value in 30 years, so t=30, and our account earns 7% interest, so r=0.07. We can plug in all of these values and solve for d to find the amount we need to deposit each month:
A(t)150,000150,000150,000d=d[(1+rn)nt−1](rn)=d[(1+0.0712)12⋅30−1]0.0712≈d[(1.00583)360−1]0.00583≈1,219.97d≈122.95
The amount you need to deposit each month is approximately $122.95.