Answers
Answer:
[tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}[/tex]
General Formulas and Concepts:
Symbols
e (Euler's number) ≈ 2.71828Algebra I
Exponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsDefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
U-SolveIntegration 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\limits^1_0 {x^5e^{x^3 + 1}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite [Exponential Rule - Multiplying]: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \int\limits^1_0 {x^5e^{x^3}e} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = e\int\limits^1_0 {x^5e^{x^3}} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-solve.
Set u: [tex]\displaystyle u = x^3[/tex][u] Differentiate [Basic Power Rule]: [tex]\displaystyle du = 3x^2 \ dx[/tex][u] Rewrite: [tex]\displaystyle x = \sqrt[3]{u}[/tex][du] Rewrite: [tex]\displaystyle dx = \frac{1}{3x^2} \ du[/tex]Step 4: Integrate Pt. 3
[Integral] U-Solve: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = e\int\limits^1_0 {x^5e^{(\sqrt[3]{u})^3}\frac{1}{3x^2}} \, du[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {x^5e^{(\sqrt[3]{u})^3}\frac{1}{x^2}} \, du[/tex][Integral] Simplify: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {x^3e^u} \, du[/tex][Integrand] U-Solve: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {ue^u} \, du[/tex]Step 5: integrate Pt. 4
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = u[/tex][u] Differentiate [Basic Power Rule]: [tex]\displaystyle du = du[/tex]Set dv: [tex]\displaystyle dv = e^u \ du[/tex][dv] Exponential Integration: [tex]\displaystyle v = e^u[/tex]Step 6: Integrate Pt. 5
[Integral] Integration by Parts: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3} \bigg[ ue^u \bigg| \limits^1_0 - \int\limits^1_0 {e^u} \, du \bigg][/tex][Integral] Exponential Integration: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3} \bigg[ ue^u \bigg| \limits^1_0 - e^u \bigg| \limits^1_0 \bigg][/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}[ e - e ][/tex]Simplify: [tex]\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Related Questions
The lines graphed below are parallel. The slope of the red line is 2/5. What is the slope of the green line?
Answers
Answer:
It's D: 2/5
Step-by-step explanation:
Parallel lines have the same slope.
Given: binom(119, 0.57)
What is the Expected Value?
Answers
Answer:
The expected value, or mean, of a binomial distribution, is calculated by multiplying the number of trials by the probability of successes. For example, the expected value of the number of heads in 100 trials of head and tales is 50, or (100 * 0.5)
Are Brainy tutors still a thing if not I’m gonna fail algebra
Answers
Answer:
I guess they are
Step-by-step explanation:
Answer:
yes they are but i cant get a hold of them srry can i have brainliest
Step-by-step explanation:
In a recent survey in a Statistics class, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 88% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course. a. What percentage of students is expected to pass the course? b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays? (Hint: the above problem is based on conditional probability concept and the Bayes theorem)
Answers
Answer:
a) 67.6% of students is expected to pass the course
b) 0.9112 = 91.12% probability that he/she attended classes on Fridays
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. What percentage of students is expected to pass the course?
88% of 70%(attended class)
20% of 100 - 70 = 30%(did not attend class). So
[tex]p = 0.88*0.7 + 0.2*0.3 = 0.676[/tex]
0.676*100% = 67.6%
67.6% of students is expected to pass the course.
b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays?
Here, we use conditional probability:
Event A: Passed the course
Event B: Attended classes on Fridays.
67.6% of students is expected to pass the course.
This means that [tex]P(A) = 0.676[/tex]
Probability that passed and attended classes on Friday.
88% of 70%
This means that:
[tex]P(A \cap B) = 0.88*0.7 = 0.616[/tex]
Then
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.616}{0.676} = 0.9112[/tex]
0.9112 = 91.12% probability that he/she attended classes on Fridays
Pls help it’s about angles
Answers
90-66=24
Sorry if it’s wrong
A hardware store received 2.5 tons of
lumber. What is the weight of the
lumber in pounds?
A 50,000 pounds
® 25,000 pounds
5,000 pounds
D 2,500 pounds
Answers
Answer:
5000 pounds
Step-by-step explanation:
Hello There!
There are 2000 pounds in 1 ton
So to convert tons to pounds we multiply by 2000
2.5x2000=5000
So 2.5 tons is the equivalent if 5000 pounds
House contents insurance is charged at the rate of $4.50 per thousand dollars worth of the contents. How much is the insurance if the contents are worth $13 600?
Answers
Answer:
188.5
Step-by-step explanation:
13 times 4.50 is 188.5 and theres 13,000
PLEASE HELP!!
The sum of two angle measures is 180°.
Which term BEST describes the two angles?
A - adjacent
B - complementary
C - supplementary
D - vertical
Answers
Answer:
supplementary
Step-by-step explanation:
the sum of two supplementary angles is 180°. They lie in a straight line.
The term BEST describes the two angles and will be supplementary. Then the correct option is C.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The types of angles are as follows:
Two angles are said to be supplementary angles if their sum is 180 degrees.When two lines intersect, then their opposite angles are equal.Two angles are said to be complementary angles if their sum is 90 degrees.In math, two points are nearby in the event that they have a typical side and a typical vertex.The sum of the two angle measures is 180°. Then the term BEST describes the two angles and will be supplementary. Then the correct option is C.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ6
Plz help!!!!!!! Image
Answers
Answer:
the third one is correct
In the finals of a singing contest at Greenvale Middle School, 300 students vote on which
contestant they liked best. The circle graph shows the results of the vote. How many
more votes did Gamba get than Ahmed?
Answers
Answer:
Gamba obtained 75 more votes than Ahmed.
Step-by-step explanation:
Given that in the finals of a singing contest at Greenvale Middle School, 300 students voted on which contestant they liked best, and Gamba got 35% of the votes while Ahmed got 10%, to determine how many more votes did Gamba get than Ahmed the following calculation should be performed:
(300 x 0.35) - (300 x 0.10) = X
105 - 30 = X
75 = X
Thus, Gamba obtained 75 more votes than Ahmed.
what is the order from least to greatest(38%,3/8,0.4,1/3,41%,0.33)
Answers
If an arithmetic progression satisfies U4=7 , U8=15 .Find U10
Answers
Answer:
U10 = 19
Step-by-step explanation:
The sequence is [tex]Ux=(x*2)-1[/tex]
x is the coefficient to U.
So, [tex]U10=(10*2)-1[/tex]
Which means [tex]U10=20-1[/tex]
Which means [tex]U10=19[/tex]
And there is your answer.
Hope this helps. Have a nice day.
Find the distance, c, between (0, –4)
and (1, 5)
on the coordinate plane. Round to the nearest tenth if necessary.
Answers
Answer:
d ≈ 9.05Steps:
d = √( (1-0)² + (5-(-4)² )
d = √( 1² + (5+4)² )
d = √( 1 + 9² )
d = √( 1 + 81 )
d = √82
d ≈ 9.05Simplify:
Camilla goes to the super market and buys two apples. each apple is $1.75. Camilla has $5.00 left. write an expression to represents this problem. Don't forget to use a variable!
Answers
Answer:
[tex] \huge \boxed{ \boxed{t - 3.5 = 5}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:equationlet's solve:a apple costs 1.75
2 apple costs 1.75×2=3.5
let her total money be t
according to the question
t-3.5=5Which two values are solutions of the inequality r≥6?
Select one:
r = 6, r = 9
r = −7, r = −8
r = 3, r = −10
r = 4, r = −2
Answers
Answer:
r = 6
r = 9
Step-by-step explanation:
HELLPP DUE BY 1pm PACIFIC HELLPP ASAP
Answers
Answer:644.355
i tried ok
Step-by-step explanation:
I got you!
Since you dont know how many individual songs he wrote, we will represent that as x. Now, to find the total amount spent on buying "x" individual songs, you would have to multiply that by the 1.29$ it costs. Therefore, with the inclusion of the 9.99$ from the album, your equation is:
50 = 1.29x + 9.99
Please help me I always sleep late doing homework and I do not want to today begging ya. You don’t have to do 1,2,3
Answers
Answer: 5, 18, 20, 25, 27, 35, 38, 40, 48, 60, 90
Step-by-step explanation: Count lol
Find the ratio a : b , if it is given that ...
5a +3b =6b
Answers
Answer:
3:5
Step-by-step explanation:
5a + 3b = 6b
5a=6b-3b
5a=3b
a/b= 3/5
a:b=3:5
need help figuring this out
Answers
Answer:
think it is d
Step-by-step explanation:
00:00
The city council in Middlefield wants to know if residents are in favor of a traffic camera at the main intersection in town. Drag tiles to match each
term to the example it best describes. Each tile may be used only once.
Representative Sample
Population
NOT a Representative Sample
Term
Example
Drivers who reside in Middlefield
Residents of Middlefield
Residents randomly chosen from the town register
Answers
Answer:
Matching Tiles with Terms:
Term Example
NOT a Representative Sample Drivers who reside in Middlefield
Population Residents of Middlefield
Representative Sample Residents randomly chosen from the
town register
Step-by-step explanation:
Population includes all the residents of Middlefield.
Representative Sample is a population subset that accurately reflects the characteristics of the population. For example, the subset of residents who are randomly chosen from the town register is an unbiased and representative sample.
NOT a Representative Sample: For example, drivers who reside in Middlefield do not represent the characteristics of the population of Middlefield.
PLEASE HELP ME!!
Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ.
n = 290, p = 1/4
Answers
20 POINTS! WILL AWARD BRAINLIEST! Which equations have only one root
Answers
Answer:
its option a i and ii plz mark me branliest
.
* 6 cupcakes for $14
* 12 cupcakes for $30
* 24 cupcakes for $54
The unit price for the 6 cupcakes is
The unit price for the 12 cupcakes is
The unit price for the 24 cupcakes is
The lowest unit price is for
Answers
Answer:
≈$2.33$2.50$2.2524 cupcakes/$54Step-by-step explanation:
Answer:
$2.33
$2.50
$2.25
24 cupcakes/$54
Step-by-step explanation:
if the price of a sweater is marked down from $80 to $68, what is the percent markdown?
Answers
Answer:
35%
Step-by-step explanation:
$28 less.
28 is 35% of 80. (28/80 = 0.35 which is 35%)
the percent markdown is 35%
Page 491 #s 6-8 6) Find the area of a square with side length 74 yard
Answers
Answer:
A=5476
Step-by-step explanation:
HOPE I HELPED
After a birthday only 1/4 cake ramains what fraction is equivalent 1/4
Answers
Answer:
2/8, 3/12, 4/24, 5/20, 6/24, 7/28, 8/32, 9/36, 10/40, etc.
Step-by-step explanation:
Anyone can help with this
Answers
Answer:
C
Step-by-step explanation:
Notice how C is the only function that is quadratic. If you expand (2x-1)^2, you get 4x^2-4x+1. Since x is raised to the power of two, it isn't linear, but quadratic.
Answer:
C
Step-by-step explanation:
i used photomath and C was not the linear one!
free BRAINLESS it could be youea
Answers
what is the negation of "x>3"?
a)=3
b.)_<3
c.)<3
Answers
Given:
The inequality is:
[tex]x>3[/tex]
To find:
The negation of the given inequality.
Solution:
The given inequality is [tex]x>3[/tex], it means all the value which are greater than 3 are included in the solution set.
Since all the values which are less than or equal 3 are not included in the solution set, therefore the negation of the given inequality is
[tex]x\leq 3[/tex]
Therefore, the negation of [tex]x>3[/tex] is [tex]x\leq 3[/tex].
Note: Option are not in proper format.
Which of the following sets represents continuous data?
A. {1, 2, 3, ...)
B. (4,7)
C. {5, 13, 16, 20, 30)
D. {..., -9, -6, -3}
Answers
Answer:
option A is your answer okk