Answer:
[tex]\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = \boxed{ \frac{4x^7}{7} - \frac{x^4}{2} + \frac{7x^2}{2} - 4x + C }[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify given integral.
[tex]\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx[/tex]
Step 2: Integrate
We can find the indefinite integral using basic integration techniques listed under "Calculus":
[Integral] Rewrite [Integration Property - Addition/Subtraction]:∴ we have found the indefinite integral.
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Learn more about integration: https://brainly.com/question/27795758
Learn more about Calculus: https://brainly.com/question/27780220
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
[tex]\dfrac{4}{7}x^7-\dfrac{1}{2}x^4+\dfrac{7}{2}x^2-4x+\text{C}[/tex]
Step-by-step explanation:
Integration is the "opposite" of differentiation.
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration (C).
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
Just add an x to the constant.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Increase the power by 1, then divide by the new power.
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}[/tex]
If the terms are multiplied by constants, take them outside the integral.
Given indefinite integral:
[tex]\displaystyle \int (4x^6-2x^3+7x-4)\:dx[/tex]
Integrate each term separately and take the constants outside the integrals:
[tex]\implies \displaystyle 4 \int x^6\:\text{d}x - 2 \int x^3 \:\text{d}x + 7 \int x \:\text{d}x - \int 4 \:\text{d}x[/tex]
Integrate, using the rules given above:
[tex]\implies 4 \cdot \dfrac{x^7}{7}-2 \cdot \dfrac{x^4}{4}+7 \cdot \dfrac{x^2}{2}-4x+\text{C}[/tex]
Simplify:
[tex]\implies \dfrac{4}{7}x^7-\dfrac{1}{2}x^4+\dfrac{7}{2}x^2-4x+\text{C}[/tex]
As one calculation:
[tex]\begin{aligned}\displaystyle \int (4x^6-2x^3+7x-4)\:dx & = \displaystyle 4 \int x^6\:\text{d}x - 2 \int x^3 \:\text{d}x + 7 \int x \:\text{d}x - \int 4 \:\text{d}x\\\\& = 4 \cdot \dfrac{x^7}{7}-2 \cdot \dfrac{x^4}{4}+7 \cdot \dfrac{x^2}{2}-4x+\text{C}\\\\& = \dfrac{4}{7}x^7-\dfrac{1}{2}x^4+\dfrac{7}{2}x^2-4x+\text{C}\end{aligned}[/tex]
PLS HELP
Which Measure of center best represents the set of data? calculate the measure of center. number of television sets in the whole: 4, 4, 3, 4, 4, 1, 3, 4, 2, 4
The question is worded weirdly, but the mean (average) is 3.3. The median is 4. The median would probably represent this better.
Step-by-step explanation:
The median is found by adding all of the numbers in the data set and then dividing by how many numbers there are.
The median is the middle number, which you find by alternately crossing out the biggest and smallest numbers.
Hope this helps!
Mr. Lawrence asks his class to round 849.354 to the nearest hundredth. Andrew says the answer is 849.35, and Paul says the answer is 849.34. Who is correct and why?
A. Paul is correct because the 4 to the right of the hundredths place is less than 5.
B. Andrew is correct because the 5 in the hundredths place is equal to 5.
C. Andrew is correct because the 4 to the right of the hundredths place is less than 5.
D. Paul is correct because the 5 in the hundredths place is equal to 5.
please help me. thanks.
[tex]~~~\text{Area of triangle} = \dfrac 12 \times \text{Base} \times \text{Height}\\\\\implies 10 = \dfrac 12 \times 5 \times w\\\\\implies w =\dfrac{20}5 \\\\\implies w = 4 ~cm[/tex]
Answer:
4cm
Step-by-step explanation:
» Concepts
The area of a triangle is how much space is in the triangle. The formula for the area of a triangle is [tex]\frac{1}{2} bh[/tex], where b = base and h = height.
» Application
We're given the area as 10 cm² and the base as 5 cm. Thus, we have to plug these values into the formula to solve for the height.
» Solution
[tex]10=\frac{1}{2} *5*h[/tex] [tex]10=\frac{5}{2}h[/tex] [tex]10*2/5=5/2(h)*2/5[/tex][tex]h=4[/tex]I need helppppppppppppppp
Answer:
91.1250 m^3
Step-by-step explanation:
The volume of a cube can be calculated if you know its side length. The formula is then volume cube = side3. This is simply the length of the side multiplied by itself two times.
Answer:
91.125
Step-by-step explanation:
The formula to find the volume of a cube is lwh. All the side lengths of a cube are equal. So in this case, 4.5 to the third power is 91.125.
I need help with this question
Answer:
Nvm you got it then thats good
Step-by-step explanation:
So well the live tutor isn't helping me well.. can one of you help me?
Answer:
The mean absolute deviation is 4
Step-by-step explanation:
The mean absolute deviation is a measure of how much a data set varies.
Step 1: Compute the mean
mean = the sum of all the terms / number of terms
mean = 94 + 86 + 95 + 99 + 88 + 90 / 6
= 552 / 6
= 92
The mean is 92
Step 2: Finding the absolute deviation
You would take each number in the data set and subtract it from the mean, take the absolute value. After you take the sum of the absolute data values
|data set #1 - mean| + |data set #2 - mean| + ... + |data set #6 - mean|
= |94 - 92| + |86 - 92| + |95 - 92| + |99 - 92| + |88 - 92| + |90 - 92|
= |2| + |- 6| + |3| + |7| + |- 4| + |- 2|
= 2 + 6 + 3 + 7 + 4 + 2
= 24
To find the mean absolute deviation you divided the sum by total number of terms...
24/6 = 4
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set (which was step 1)
Let me know if you have any questions !
I applied to be a live tutor, Hope to impove the experience :)
Have a nice day, feel free to give me feedback
what is 3\8 x 2\4 PLEASE HURRY
Answer:
3/8
Step-by-step explanation:
3/8*2/4=6/24=3/8
I need help ASAP!!!!!!!!!!!!!!!!
Answer:
Katie wants to know if people prefer cats or dogs. She is unable to ask all 3,000 people in her area, so she randomly samples 350. If 174 people say they prefer dogs, what percent of the random sample likes cats?
Step-by-step explanation:
A population size means there are 3,000 total. A sample size means that 350 are sampled.
SOMEONE HELP PLEASEE!!!
Answer:
To the left 10 units and down 8
Step-by-step explanation:
How many solutions do both of these equations have?
1.) 2x-9=-5
2.) 4x-6y=2
Answer: 1 solution
Step-by-step explanation:
Tamar is thinking of a number in the hundredths. Her number is greater than 0.8 and less than 0.9. The greatest digit in the number is in the hundredths place. What number is Tamar thinking of? Explain.
Help? I’m just a poor unfortunate kid! I can not be expected to do dis math!
Helpppp?
Please? Anyone? Hear my cry? Help me from the pit of anguish and end my torment!
Thank you
Answer:
For the second one, Cancel the common factor of 8x - 16 and 2. which equals 4x - 8.
For the first one, The answer will be 7-9 simplified into 0.7
Step-by-step explanation:
Comment if wrong
(pls help!! my teacher whats me to pass this) for the point S(-3, 3), where will the image of this point be located after applying the translation rule 3 units on the x-axis and -3 units on the y-axis?
Answer: (0, 0)
Step-by-step explanation:
start at (-3, 3)
go 3 units right
(0, 3)
go 3 units down
(0, 0)
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles:
An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 54 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?
(π = 3.14)
Answer:
4578.12 inches squared
Step-by-step explanation:
so 54 x 27 x 3.14 for pie equals 4578.12 that's the awnser but put it in inches squared ok so 4578.12 inches squared
Mr. Milson donates $3,599 by check for Haiti relief fund.
The amount in his account is $108,458. What will be the
balance in his account once the check is released?
Answer:
His remaining balance will be $104,859
Step-by-step explanation:
$108,458 - $3,599 = $104,859
In the diagram of an apartment, each inch represents 6 feet. Which is the area of the apartment's balcony?
Answer:
72 square feet
Step-by-step explanation:
Since you already know the 2 inches, you just need to find out the other side, and by subtracting the longer side 6 inches, to the shorter side on the furthest side 5 inches, you get 1 inch. And since each inch represents 6 feet, the final equation would be 12 (2x6) x 6 (1x6). So the answer would be 72 square feet.
Please solve fast NOT A TEST!!!!!!!!
9.5 × 106 written in standard notation?
Answer:
Since our exponent, 6, is positive, we move the decimal place 6 places to the right to get the standard notation.
= 9,500,000
Let me know if you have a concern or question.
What does this symbol mean in math ≈ ?
Solve the following inequality. Check your answer and graph your answer. -5(k-3) ≤ -25. Thank you in advance!
Answer:
k>=8
Step-by-step explanation:
Jenna placed her finger on the origin of a regular coordinate plane. She marked
a point after moving her finger 8 units to the left and 3 units up. What is the order
pair of the point that Jenna marked?
Answer:
(-8, 3)
Step-by-step explanation:
someone help meeeeeee
Answer:
can you retake a picture of your question
Only thirty percent of the ten contestants had the correct answer. How many did not have the correct answer?
pls help
Step-by-step explanation: the answer should be 70% because to find the answer you subtract 100% minus 30% getting an answer of 70% so hopefully that is the correct answer and please give me brainliest if you want
:DDDDDDDDDDDDD
Answer:
7
Step-by-step explanation:
(Find the Probability Question)
Choose 2 girls from a class of 12 boys and 8 girls.
Step-by-step explanation:
what should be the question ?
how many different pairs of 2 girls can you pick out of 8 ?
what is the probability that a specific girl is in the picked pair ?
or is it : if you pick randomly 2 students from the class, what is the probability to have picked 2 girls ?
and there are more options.
but I assume the problem is the picking randomly 2 students.
so, it is 20 students (12 + 8). if we pick 1 student, we have a chance of 12/20 = 3/5 to pick a boy, and a chance of 8/20 = 2/5 to pick a girl.
in our experiment we pick 2 students in a row without returning the first pick into the main pool.
the probabilty for the first pick to be a girl is, as mentioned, 2/5 or 0.4.
for the second pick we have only 7 out of 19 choices to pick a girl. so, the probability to pick a girl now is 7/19.
the combination of both (non-overlapping) probabilities is done via multiplication, and the probabilty to pick 2 girls is :
2/5 × 7/19 = 2×7 / 5×19 = 14/95 = 0.147368421...
What is the value represented by the letter A on the box plot of data?
5, 20, 40, 50, 50, 85
Answer:
The value represented by the letter A on the box plot of data is 5
Step-by-step explanation:
The set of data is
{5, 20, 40, 50, 50, 85}
In the given box plot,
A = Minimum value
B = First quartile
C = Median
D = Third quartile
E = Maximum value
Since the minimum value of the set is 5, therefore the value represented by the letter A on the box plot of data is 5.
5) Solve for x and find both angle measurements -
Answer:
x = 30
(2x)° = 60°
x = 30°
Step-by-step explanation:
The two angles combined is a right angle, and a right angle is 90°, so we can put that into this equation:
2x + x = 90 which is the same as 3x = 90 because 2x + x = 3x
3x = 90
divide both sides by 3 so you can get x by itself
3x divided by 3 = x
90 divided by 3 = 30
you get x = 30
since x = 30, 2x is the same as 2 times 30, and that is 60.
In which data set is the mean less than the median?
Use each table to find the requested ratio.
Heck did I do wrong!?!?! IXL sucks
Answer:
∠G, ∠HGI, ∠IGH
Step-by-step explanation:
» Concepts
To name an angle, you MUST include the vertex either in the middle or have it standing by itself. To clarify, you can either call this angle ∠G, ∠HGI, or ∠IGH because they all include the vertex, G, in the middle or by itself. You put ∠HIG, which is incorrect because the vertex is not I.
Answer the question below follow the instructions if you would please present your answer like
Question A: ENTER ANSWER HERE
if you wouldn't mind!
Answer:
1: 25
2: 8
3: 33.6
4: 27
5: 68.4
Answer:
25833.62768.4Step-by-step explanation:
Follow the Math Rule of PEMDAS
[tex][4*(4+3)]-3\\(4*7)-3\\28-3\\25[/tex]
[tex][(7-5)/\frac{1}{2}]*2\\((2)/\frac{1}{2})*2 \\4 * 2\\8[/tex]
[tex](5.4+3)*(6-2)\\7.4*4\\33.6[/tex]
[tex][9/3 +6]*3\\(3 + 6)*3\\(9)*3\\27[/tex]
[tex](4+3.2)*[(9-2)+2.5]\\(7.2)*[(7)+2.5]\\(7.2)*[9.5]\\68.4[/tex]