evaluate the following definite integral
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
A catering company needs 8.75 Ib of shrimp for a small party. They buy 3 2/3 Ib of jumbo shrimp, 2 5/8 Ib of medium-sized shrimp, and some mini-shrimp. How many pounds of mini -shrimp do they buy?
Need help ASAP!!!!!!!!!!
Answer:
the last two
Step-by-step explanation:
Please solve the following. Solve for X. PLEASE HELP
Answer:
8
Step-by-step explanation:
(x+4)/x=24/16
24x=16x+64
8x=64
x=8
Dominick and Janelle are working to simplify the expression 2c + 4 + c + 6. Janelle simplifies her expression to 2c + 10, while Dominick simplifies his to 3c + 10.
Answer:
3c + 10
Step-by-step explanation:
1c = c
2c + 4 + c + 6
(combine like terms)
3c + 10
Answer:
Dominic is right
Step-by-step explanation:
equation:
2c + 4 + c + 6
combine like terms:
2c + c = 3c
4 + 6 = 10
new equation:
3c + 10
If Fx) = 8x, which of the following is the inverse of F(x)?
Answer
y=x/8
Step-by-step explanation:
f(x)=8x
f(x)=y
y=8x(interchange the values)
x=8y(divide by 8 both sides)
y=x/8
I need help please.
Answer:
its b
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Because it is invert.
PLEASE HELP DUE IN 3 minutes
130-139=4
140-149=7
150-159=4
160-169=5
What is the range of the data set? *
2 points
53, 39, 123, 59, 25, 79, 88
84
53
123
98
25
Answer:
25
Step-by-step explanation:
range = largest value - smallest value (123-25)
A population has a mean of 125 and a standard deviation of 16. A sample of 64 observations will be taken. The probability that the sample mean will be between 122.4 and 126.1 is
Answer:
0.61204
Step-by-step explanation:
μ = 125 ; σ = 16 ; n = 64
Probability that mean will be between 122.4 and 126.1
Z = (x - μ) / σ/sqrt(n)
x = 122.4
Z = (122.4 - 125) ÷ 16/sqrt(64)
Z = - 2.6 ÷ 2 = - 1.3
P(Z < - 1.3) = 0.0968
x = 126.1
Z = (126.1 - 125) ÷ 16/sqrt(64)
Z = 1.1 ÷ 2 = 0.55
P(Z < 0.55) = 0.70884
P(Z < 0.55) - P(Z < - 1.3)
0.70884 - 0.0968
= 0.61204
The parent function is given by f(x) = x^2
Choose the BEST description for f(x - 3)+2.
Expand the following expression −7(5x−8)
Select one:
5x+56
35x−8
56−35x
21x
there are 65 cookies in a jar. the probability of randomly choosing an oatmeal cookie from the jar is 40% how many of the cookies are oatmeal cookies pls help
Answer:
25
Step-by-step explanation:
find the area of the figure use 3.14 for pie
3.5 liters into kiloliters
Answer:
.0035 kiloliters
Step-by-step explanation:
1 liter = 0.001 kiloliters
3.5 liters x .001 = .0035 kiloliters
or just use calculator bro
what is x in 5x - ((2x-1)÷2) = 5
Answer:
5x - ((2x-1)÷2) = 5-----(1)
(1) multiply by 2;
2 *(5x - ((2x-1)÷2) = 5)
10x - (2x-1) = 10
10x - 2x + 1 = 10
8x + 1 =10
8x = 10-1
x=9 /8
Step-by-step explanation:
Answer:
x = 9/8
Step-by-step explanation:
5x - ((2x - 1) ÷ 2) = 5
2 × (5x - ((2x - 1) ÷ 2) = 5
10x - (2x-1) = 10
10x - 2x + 1 = 10
8x + 1 = 10
8x + 1 - 1 = 10 - 1
8x = 10 - 1
8x = 9
8x ÷ 8 = 9 ÷ 8
x = 9 ÷ 8
x = 9/8 or 1 and 1/8
$200 in a savings account. The interest rate is 3%. Determine the exact amount of money that will be in the
account after the following amounts of time.
a) 2 months: b) 6 months:
c) 11 months: d) 1 year:
e) 2.5 years: f) 5 years:
Answer:
what
Step-by-step explanation:
What is the slope of a line perpendicular to a line that contains the points (-8,-4) and (0,-8)
Answer:
I hope some of these help (examples)
Step-by-step explanation:
Line AB contains points A (1, 2) and B (−2, 6) The slope of line AB is
a)zero
b)undefined
c)positive
d)negative
The equation of line CD is (y−3) = − 2 (x − 4). What is the slope of a line perpendicular to line CD?
Line CD contains points A (4, 6) and B (−2, 6). The slope of line CD is
Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (−2, 2). Lines QR and ST are
The equation of line QR is y = negative 1 over 2x + 1. Write an equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6).
The equation of line CD is y = −2x − 2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5).
Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (−2, 2). Lines QR and ST are
parallel because the product of the slopes is −1
perpendicular because the product of the slopes is −1
parallel because the slopes are the same
perpendicular because the slopes are the same
Question 2
(06.02 LC)
The equation of line CD is (y−3) = − 2 (x − 4). What is the slope of a line perpendicular to line CD?
1 over 2
2
negative 1 over 2
−2
Question 3
(06.02 LC)
Line CD contains points A (4, 6) and B (−2, 6). The slope of line CD is
zero
undefined
positive
negative
Question 4
(06.02 MC)
The equation of line QR is y = negative 1 over 2x + 1. Write an equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6).
y = 2x + 16
y = negative 1 over 2x + 17 over 2
y = − 1 over 2x + 7 over 2
y = 2x − 4
Question 5
(06.02 MC)
The equation of line CD is y = −2x − 2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5).
y = −2x + 13
y = negative 1 over 2x + 7
y = 1 over 2x + 3
y = − 2x − 3
On the first question, the formula would be m=\frac{y2-y1}{x2-x1} and the value we got is -4/3, so D.
On the second quesiton, the slope in the given equation of the line is -2, its negative reciprocal is 1/2, so A.
On the third question, use the slope formula above and the value you would get is zero, so A.
On the fourth question, the equation of the line perpendicular to line QR is y=2x+b, to find b, just substitute the point (5,6) to the equation. That would make b = -4. the final equation of the line would be: y=2x-4, so D.
On the fifth question, the equation of the line parallel to line QR is y = -2x + b. substitute the point (4,5) to the equation, and you'll get b = 13. the final equation of the line would be y=-2x+13, so A.
D,A,A,D,A
1) Determine the slope of the line that is perpendicular to the equation below.
y = -3x + 4
Type your answer as a reduced fraction, if necessary, like this: 3/4
2) Which line is parallel to the line with this equation?
3x – 4y = 24
A) 8y-6x=32
B) 3x-5y=25
C) y=-3/4x -6
D) y+3 = 3(x-4)
3) Determine which equation is in slope-intercept form for the line that passes through (5, 0) and is perpendicular to the line below.
y = -5/2x + 6
A) y=-2/5x - 2
B) y=5/2x+2
C) y=5/2x-2
D) y=2/5x-2
4) Line 1 contains the points (6, -5) and (2, 7). Which of the given pairs of coordinates could be contained by Line 2 if Line 1 is parallel to Line 2?
HINT: Remember that two parallel lines share NO points.
A) (2,7) and (11,10)
B) (6,-5) and (-1, 3)
C) (9,8) and (6, 9)
D) (5,6) and (9, -6)
5) What value should replace the "?" to make the equations parallel?
Type your answer as a reduced fraction, using the "/" symbol to separate the numerator and denominator, like this: 2/5
y=5/3 x - 8
y=? x + 9
6)Determine whether the pair of lines is parallel, perpendicular, or neither.
y = 7x and y – 28 = 7(x – 4)
A) parallel
B) perpendicular
C) Neither
1) m=-2
2) C) y=-3/4x -6
3) D) y=2/5x-2
I hope this helps:)
Use the distributive property to write an equivalent expression. 4(2x+3)
Answer:
20x
Step-by-step explanation:
4(2x+3)
4(5x)
4x5x
20x
Please indicate which type of sampling design is most appropriate for each of the following studies. The choices are SRS, stratified random sampling, and matched pair design.
a. A campus newspaper randomly selects 20 common Spring Break destinations and surveys the residents about their attitudes of students spending Spring Break in their city.
b. A developer in West Lafayette wants to know if students who are renting off-campus like their apartment complex. They chose 10 students who lived in 5 different complexes.
c. A researcher wants to know the difference in time it takes to apply brakes between people who are not talking on the phone and people who are talking on a hands-free cell phone. She chose 100 individuals and then drive both ways in a simulator and measured their responses. A student organization has 55 members. Out of these members, five are selected randomly to attend a national conference.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
In point 1
The random selection stratified: although 50 statements belong to 5 different groups.
In point 2:
Coincide pair design: As we're in the SAME location to measure the difference between the downstream and upstream fractures. Although when calculating a top-down split they need only to calculate the low-up split which corresponds to the top-down split.
In point 3:
Matched layout: As 100 individuals were chosen and ALL were required to give BOTH and document certain responses.
In point 4:
SRS: RANDOMLY has also been selected since 20 spring break goals.
Solve the following question:
Q1: A family has booked a long holiday in Skragness, where the probability of rain on any particular day is 0.3.
a) Find the probability that the first day to rain will be on the third day of their holiday.
b) Find the probability chance that it will not rain for the first 2 weeks of their holiday.
[hint: X~Geo(0.3) a) P(X=__), b) P(X<__)]
Q2: If G~B(42, 7/12)
a) Find E(G) and Var(G) giving your answer as a fraction or mixed number
b*) Find P(G=20) correct to 3 significant figures.
Answer is in the photo. I can only upload it to a file hosting service. link below!
tinyurl.com/wpazsebu
The manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly less than 9 minutes. A random sample of 28 customers was taken. The average length of calling time in the sample was 8.1 minutes with a standard deviation of 2.9 minutes. At a 0.05 level of significance, it can be concluded that the mean of the population is:
Answer:
Step-by-step explanation:
4. Determine the volume of the eraser below. 3 in 1.5 in eraser 1 in
Answer:
volume = 4.5 in³
Step-by-step explanation:
V = L x W x H
V = 3 x 1.5 x 1 = 4.5
Maximize −4x + 5y + 70 subject to the constraints:
2x + y ≤ 8
x + 3y ≥ 5
x + y ≤ 6
x ≥ 0,
y ≥ 0
a. Fix any constraints, as needed, and then convert the linear programming problem into a system of linear equations.
b. Give a fully labeled initial tableau, and circle the pivot element.
Answer:
Step-by-step explanation:
[tex]\text{To maximize -4x + 5y + 70 subject to } \\ \\ 2x + y \le 8 --- (1) \\ \\ x + 3y \ge 5 --- (2) \\ \\ x + y \le 6----(3) \\ \\ x \ge 0, y \ge 0[/tex]
[tex]\text{From above equationn (1)} : 2x + y = 8 \\ \\ \text{Divide boths sides by 8} \\ \\ \dfrac{2x}{8} + \dfrac{y}{8} = \dfrac{8}{8}[/tex]
[tex]\dfrac{x}{4} + \dfrac{y}{8} = 1 \\ \\ x = 4; y = 8[/tex]
[tex]\text{From above equationn (2)} : x + 3y = 5 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{5} + \dfrac{3y}{5} = \dfrac{5}{5} \\ \\ x = 5; \ y = 1.66[/tex]
[tex]\text{From above equation (3)} : x + y = 6 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{6} + \dfrac{y}{6} = \dfrac{6}{6} \\ \\ x = 6; \ y = 6[/tex]
[tex]\text{From the image attached below, we can see the representation in the graph}[/tex]
- [tex]\text{Now from equation (1) ad (III)} \\ \\ 2x + y = 8 \\ \\ x+y = 6[/tex]
[tex]x[/tex] [tex]= 2[/tex]
[tex]From : x + y = 6 \\ \\ 2 + y = 6 \\ \\ y = 6-2 \\ \\ y =4[/tex]
[tex]\text{From equation (1) and (II) } \\ \\ \ \ 2x + y = 8 \\ - \\ \ \ x + 3y = 5 \\ \\[/tex]
[tex]-5y = -2 \\ \\ y = \dfrac{2}{5} \ o r\ 0.4 \\ \\ From : 2x+ y = 8 \\ \\ 2x = 8 - \dfrac{2}{5} \\ \\ x = \dfrac{ 8 - \dfrac{2}{5} }{2} \\ \\ x = 3.8[/tex]
please help ill give brainliest
Which graph best represents f(x)=6(3)x. PLEASE
Answer:
Hi! You have not shown any options, but your graph should look like this
Step-by-step explanation:
I need help please.
Answer:
B
Step-by-step explanation:
PLSSS HELP ASAPPPPPP
it will be A.25
Step-by-step explanation:
hope its right
Other Academics
4: Assessment Form A
Henry sells rings for $8 each. His expenses are $1.50 per ring, plus $91 for supplies. How many rings does he need to sell for his revenue to equal his
expenses?
A 140
B. 9
C. 10
D. 14
there 2 parts to the question
Answer:
a) ∠PNQ=40°
b) ∠POQ=80°
Explanation:
The Inscribed Angle Theorem proves that an inscribed angle is half of the intercepted arc length. From that information, we can determine the angle of PNQ with ∠PNQ=[tex]\frac{1}{2}[/tex]QP or ∠PNQ=[tex]\frac{1}{2}[/tex](80). Multiply those two to get 40. Because the central angle is equal to the measure of its intercepted arc length. So, we know that ∠POQ is 80°.