Answer:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C[/tex]
Step-by-step explanation:
we want to integrate the following integration:
[tex] \displaystyle \int {x}^{2} \cdot {e}^{x} dx[/tex]
notice that, the integrand is in the multiplication of two different function in that case we can consider integration by parts given by:
[tex] \rm \displaystyle \int u \cdot v \: dx = u \int vdx - \int u' \left( \int v dx \right)dx[/tex]
where u' can be defined by the differentiation of u
now we have to choose our u and v
which can be chosen by using the guideline:ILATE Inverse trig. , Logarithm, Algebraic expression, Trigonometry, Exponent.
since x comes first thus,
[tex] \displaystyle u = {x}^{2} \quad\text{and} \quad v = {e}^{x} [/tex]
by figuring out the defferentiation of u,we acquire:
[tex] \displaystyle u' = 2x[/tex]
altogether we get:
[tex] \rm \displaystyle \int {x}^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int 2x \left( \int {e}^{x} dx \right)dx[/tex]
by figuring out the parentheses integration
we get:
[tex] \rm \displaystyle \int x^2 \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int2x \cdot {e}^{x} dx[/tex]
now we again have integration of two different functions so let's choose our u and v once again which can be done using the guideline
[tex] \displaystyle u = 2x \quad\text{and} \quad v = {e}^{x} [/tex]
by figuring out the defferentiation of u
we acquire:
[tex] \displaystyle \: u' = 2[/tex]
altogether we get:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x \int{e}^{x} dx- \int2 \left( \int{e}^{x}dx \right) dx \right)[/tex]
by solving parentheses we get
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x {e}^{x} - 2 e^{x} dx \right)[/tex]
by figuring out the integral we get:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- \left( 2x {e}^{x} - 2 e^{x} \right)[/tex]
remove parentheses:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} [/tex]
at last we of course have to add constant of integration:
[tex] \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C[/tex]
and we are done!
Answer:
[tex]\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigTabular IntegrationStep-by-step explanation:
*Note:
The answer below me is correct, but there is a simpler method of obtaining the answer.
Step 1: Define
Identify
[tex]\displaystyle \int {x^2e^x} \, dx[/tex]
Step 2: Integrate
Use tabular integration.
[Integrand] Differentiate/Integrate [Tabular Integration]: [tex]\displaystyle \\\begin{center}\begin{tabular}{ c | c }\line{u & dv} \\\cline{1 - 2} x^2 & e^x \\\ 2x & e^x \\\ 2 & e^x \\\ 0 & e^x\end{tabular}\end{center}[/tex]Write out expansion [Tabular Integration]: [tex]\displaystyle \int {x^2e^x} \, dx = x^2e^x - 2xe^x + 2e^x + C[/tex]Factor: [tex]\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
It takes you 3 hours to drive to a concert 135 miles away. You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads. Write a system of linear equations that represents this equation. Use x to represent the number of hours driving on a highway and y to represent the number of hours driving on other roads.
Answer:
x + y = 3 (1)
55x + 40y = 135 (2)
Step-by-step explanation:
Since x to represent the number of hours driving on a highway and y to represent the number of hours driving on other roads and the total time for driving is 3 hours,
x + y = 3 (1)
Also, You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads, the distance moved on highways is 55x and the distance moved on the rest of the roads is 40y (since distance = speed × time).
Since the total distance moved is 135 miles, we have
55x + 40y = 135 (2)
So, the system of linear equations that represent the situation is
x + y = 3 (1)
55x + 40y = 135 (2)
Help i will give u brainlest
Erin buys gas at a gas station for $4 a gallon. There is a sale going on at the gas station so that anyone who buys more than 5 gallons of gas only has to pay $3 a gallon for each gallon over 5 gallons. If a person buys more than 10 gallons of gas, each gallon over 10 gallons is only $2 a gallon for every gallon over 10 gallons but less than or equal to 15 gallons.. Erin's tank holds 12 gallons of gas.
Answer:
39$
Step-by-step explanation:
20+15+4=39$
Mhanifa can you please help? I will mark brainliest! This is due soon!
Answer:
In a n -sided polygon, sum of its interior angles is (n−2)×180∘ , hence sum of the interior angles in a convex hexagon is (6−2)×180∘=720∘ .
Answer:
Q1Sum of interior angles on n-sides polygon is:
S = (n - 2)*180°Sum of interior angles of a hexagon (6-sided polygon):
S = (6 - 2)*180° = 4*180° = 720°Q9Sum of exterior angles of any polygon is 360°
Each exterior angle of a pentagon is:
360°/5 = 72°Help me with this please
Can some please help me?
First person gets Brainliest, 10 points!
Answer:
oof iiiiiimmmmmmmmmso sorrry
Amelia bought a t-shirt for $15 and 3 pairs of pants. She spent a total of $117. Which equation matches this problem?
Answer:
The answer of the equation is 15x+3x=117.
Step-by-step explanation:
Help thanks ☺️..... ........
Answer and Step-by-step explanation:
The area of the tile is 9.
To find the area, we multiply the side by another side.
3 times 3 is equal to 9.
#teamtrees #PAW (Plant And Water)
A square has its dimensions changed by a scale factor of 3. If the new area is 225 square inches, what was the area of the original square?
10 seconds : 1 minute as a fraction in simplest form
Answer:
1/6
Step-by-step explanation:
60 seconds is one minute, so 10 seconds is one-sixth of a minute.
Answer:
Was there supposed to be an attachment?
Step-by-step explanation:
I think there was supposed to be an object but um, i will try my best with the info there is.
10 seconds in a fraction of a whole minute is 1/6. (10/60 = 1/6)
1 minute as a fraction is just (60/60 or 1)
What are the coordinates of the two points on the line? Select all that apply.
Answer:
choice 1 and choice 3) (1,8) and (7,1)
Step-by-step explanation:
4 x 1/3 as a fraction
Answer:
4/3 = 1⅓
improper from and it's mixed fraction
Step-by-step explanation:
4*1/3
4/3 = 1⅓
Use the distributive property to factor the expression below.
544 y - 12 x 7
I’ll give brainiest whoever get it right!
ANYONE IM RUNNING OUT OF TIME!!!!!
Answer:
Y= -5/2x+3
Step-by-step explanation:
A perpendicular slope is always opposite (meaning if the original is negative, then it is positive and vice versa) and reciprocal (meaning the numerator and denominator of the original are flipped).
The y intercept I found by applying the slope to the point given.
What’s the answer of this problem, you
Answer:
A = 216 [tex]m^{2}[/tex]
Step-by-step explanation:
Trapezoid area = [tex]\frac{a+b}{2}h[/tex] = [tex]\frac{11 m+25 m}{2}*12 m[/tex] = 216 [tex]m^{2}[/tex]
Determine the volume of this prism
Answer:
200cm cubed
Step-by-step explanation:
Remember that volume of a rectangular prism is length x width x height
Answer: A) 200
Step-by-step explanation: The volume of a prism is length x width x height. Substitute the variables in this given prism into the equation.
Length = 10
Width = 5
Height = 4
V = 10 x 5 x 4 = 200
can anyone help me with this?
A 2-column table with 5 rows. Column 1 is labeled Number of Siblings with entries 0, 1, 2, 3, 4. Column 2 is labeled Students with entries (Jenn, Bill, Rosa, Juan), Cho, (Damon, Mike, Lisa, Lupe, Maggie), blank, Greg.
A small class took a survey of the number of siblings each student has. The data are shown in the table.
Which data representation would be most appropriate to represent each student who has a given number of siblings?
line graph
line plot
bar graph
stem and leaf plot
Answer:
line plot
Step-by-step explanation:
easy algebra question
Answer: 235 people got a real one
Step-by-step explanation:
Toby has created a map of his neighborhood. When he drew the map he noticed his house, his friend's house, and the playground formed a right triangle
Since you started recording it on your calendar. There have been 112 sunny and 42 rainy days. What has been the rainy day to sunny day ratio?
Answer: 3:8
Step-by-step explanation:
Number of rainy days = 42
Number of sunny days = 112
To calculate the rainy day to sunny day ratio, we can first use the numbers given as fraction and divide to its lowest term. This will be:
= Number of rainy days / Number of sunny days
= 42 / 112
= 3/8
Therefore, the ratio of rainy days to sunny days will be 3:8
Does any body know how to find Late Payment in Mathematics.
Answer:
I don't believe there is a standard formula for late payments. The late payment charge would vary by the lending institution. Some may have their own formula and some may have a set charge.
Step-by-step explanation:
HELP PLS
Jeremy drew out the route he will hike over a 3-day period on the coordinate grid below. He will hike from Point A to Point B and from Point B to Point C on the first two days. On day 3, he will hike directly from Point C to Point A.
If each grid unit represents a distance of 1 mile, what is the distance Jeremy will need to travel between Point C and Point A?
The distance Jeremy will need to travel between Point C and Point A 19.69 miles.
We have given that,
Jeremy drew out the route he will hike over a 3-day period on the coordinate grid below.
He will hike from Point A to Point B and from Point B to Point C on the first two days.
On day 3, he will hike directly from Point C to Point A.
We have to determine the distance Jeremy will need to travel between Point C and Point A.
What is the distance formula?
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
d = distance
(x_1, y_1) = coordinates of the first point
(x_2, y_2) = coordinates of the second point
(4,9)=(x_1,y_1)
(-4,-9)=(x_2,y_2)
[tex]d = \sqrt{(-4 - 4)^2 + (-9-9)^2}\\d=\sqrt{(8)^2+(18)^2} \\d=2\sqrt{97}\\ d=19.69[/tex]
Therefore, The distance Jeremy will need to travel between Point C and Point A 19.69 miles.
To learn more about the distance visit:
https://brainly.com/question/2854969
#SPJ1
2 x (6 divied 2 dived 8) - 4
Answer:
18
Step-by-step explanation:
6/2=3+8=11
11*2=22
22-4=18
Use this to help you next time!
Paranthesis
Exponets
Multiplication
Divison
Add
Subtract
Hope this helps!
The area of a circle is 2.5434 square meters. What is the circle's radius?
Answer:
r= 0.899m
Step-by-step explanation:
A= [tex]\pi[/tex]r²
r=√A/[tex]\pi[/tex]
Answer:
0.8468686471
Step-by-step explanation:
Area of a circle = π r²
2.2534= 3.142*r^2
0.7171865054=r^2
r=Square root of 0.7171865054
=0.8468686471
Find the area of the trapezoid
area = ( top rule + bottom rule ) × height / 2
area = ( 2 + 3 ) × 4 / 2
area = 5 × 4 / 2
area = 20 / 2
area = 10
Four less than x = ??
Answer:
x-4
Step-by-step explanation:
Answer:
x-4
Step-by-step explanation:
1. Jemima wants to make chocolate chip walnut brownles. Chocolate chips come in a 12oz bag that costs $3. Walnuts
come in a 4oz bag that costs $2. If Jemima needs three pounds of chocolate chips and walnuts combined, and has $15
to spend, how many bags of each can she buy?
Answer:
4 bags of chocolate chips and 1 bag of walnuts.
Step-by-step explanation:
Find how many ounces are in 3 pounds:
16 oz = 1 lb
16 oz × 3 = 3 lbs
48 oz = 3 lbs
Variable x = number of chocolate chips
Variable y = number of walnuts
4x + 1y = 15
Keep in mind it must equal up to 48 oz and be $15 or under.
4 bags × 12 oz = 48 oz
1 bag × 4 oz = 4 oz
48 oz + 4 oz = 52 oz > 48 oz
4 bags × $3 = $12
1 bag × $2 = $2
$12 + $2 = $14 < $15
Both requirements have been met.
An architect has designed a new hotel shaped like a giant rectangular pyramid. The base of the model for this hotel measures 20 inches by 30 inches, and is 25 in. tall. What is the volume of the pyramid?
Answer:
Volume of pyramid = 5000 cubic inches.
Step-by-step explanation:
Given the following data;
Length = 20 inches
Width = 30 inches
Height = 25 inches
To find the volume of pyramid;
Mathematically, the volume of a pyramid is given by the formula;
[tex] Volume = \frac {1}{3} * base \; area * height [/tex]
First of all, we would determine the base area;
Base area = length * width
Base area = 20 * 30
Base area = 600 in²
Substituting into the formula, we have;
[tex] Volume = \frac {1}{3} * 600 * 25 [/tex]
[tex] Volume = 200 * 25 [/tex]
Volume of pyramid = 5000 cubic inches.
PLEASE HELP MEEE!!!!!