Answers
Answer:
\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = \boxed{ \frac{4x^7}{7} - \frac{x^4}{2} + \frac{7x^2}{2} - 4x + C }\)
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]:
\(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Step-by-step explanation:
Step 1: Define
Identify given.
\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx\)
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]:\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = \int {4x^6} \, dx - \int {2x^3} \, dx + \int {7x} \, dx - \int {4} \, dx\)[Integrals] Rewrite [Integration Property - Multiplied Constant]:
\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = 4 \int {x^6} \, dx - 2 \int {x^3} \, dx + 7 \int {x} \, dx - 4 \int {} \, dx\)[Integrals] Apply Integration Rule [Reverse Power Rule]:
\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = 4 \bigg( \frac{x^7}{7} \bigg) - 2 \bigg( \frac{x^4}{4} \bigg) + 7 \bigg( \frac{x^2}{2} \bigg) - 4x + C\)Simplify:
\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = \boxed{ \frac{4x^7}{7} - \frac{x^4}{2} + \frac{7x^2}{2} - 4x + C }\)
∴ we have found the given integral.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Related Questions
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to solve quadratic equation?8x² + 16x + 3 = 0
using Quadratic formula
The following steps are involved
\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)
\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)
\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)
\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)
\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)
\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)
\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)
\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)
\(x = -0.209431\)
or
\(x = -1.79057\)
Therefore, the steps peter could follow will give the result
\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)
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Question 4
Two diagonally opposite vertices of a square on a coordinate grid are located at (-5,7). (1,1). What is the
perimeter of the square? (7.G.6)
1p
Answers
Check the picture below.
PLEASE HELP ILL GIVE LIKE 60 POINTS Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a coordinate plane.
(3,1), (10,8), (5,13)
The orthocenter is what? IM LOOKING FOR PART B BTW TYSMMMMMM
Answers
Answer:
An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. The orthocenter of a triangle is that point where all the three altitudes of a triangle intersect.
Step-by-step explanation:
Hope this Helped! :)
Aiden leans a 30-foot ladder against a wall so that it forms an angle of 78^{\circ} ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
6.2 approx i believe
Step-by-step explanation:
5/30 divided by 5/11
Answers
Answer:
0.33
Step-by-step explanation:
I have 2 questions
1. my final for one of my classes is 150 points and I need to score at least a 53.16% on the final exam, how many points of the overall 150 would I need to get correct.
2. for my other final it is worth 200 points and I need to score at least a 44.45% on the final exam, how many points of the overall 200 would I need to get correct.
Answers
2. You need to get around 89 points
this leads us to a sturm-louiville problem in x. in each case the general solution in x is written with constants a and b
Answers
An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.
The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.
For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following
form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.
The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.
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A regular pentagon has a side length of 2x+9. A square has a side length of 3x
Answers
The possible solution for x can be 22.5.
We are given that the side of the regular pentagon = 2 x + 9
So, the perimeter will be:
P ( Regular pentagon) = 5 × ( 2 x + 9 )
P ( Regular pentagon) = 10 x + 45
Also, we are given that the side of a square is 3 x
Perimeter will be:
P ( square) = 4 × 3 x
P ( square) = 12 x
Now, we are given that P ( Regular pentagon) = P ( square)
So, we get that:
10 x + 45 = 12 x
12 x - 10 x = 45
2 x = 45
x = 45 / 2
x = 22.5
Therefore, the possible solution for x can be 22.5.
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Your question was incomplete. Please refer the content below:
A regular pentagon has a side length of 2x-9. A square has a side length of 3x. If both polygons have the same perimeter, what is a possible solution of x?
if you toss a die once, consider the two events , you get a 5 OR 6. YOU GET AT MOST 3. are these events independent, explain WHY OR WHY NOT
Answers
Answer: These events are independent.
Step-by-step explanation:
Two events are considered independent if the outcome of one event does not affect the outcome of the other event. In this case, getting a 5 or 6 on a dice toss and getting at most 3 on a dice toss are independent events.
This is because the probability of getting a 5 or 6 is 2/6 or 1/3, which is completely unrelated to the probability of getting at most 3, which is 3/6 or 1/2. The outcome of getting a 5 or 6 does not affect the probability of getting at most 3, and vice versa. Therefore, these events are independent.
find the area of the shaded region. Note that the total radius from the center out to the edge of the shaded region is 8+3=11.
Answers
To determine the area of the shaded region we notice that it is equal to the area of the outer circle minus the area of the inner circle.
Recall that the area of a circle is given by the following formula:
\(A=r^2\pi,\)where r is the radius of the circle.
Using the above formula, we get:
\(\begin{gathered} A_{innercircle}=(3cm)^2\pi, \\ A_{outercircle}=(11cm)^2\pi. \end{gathered}\)Therefore, the area of the ring is:
\(A=(121-9)cm^2\pi=112\pi cm^2.\)Answer:
\(\begin{equation*} 112\pi cm^2. \end{equation*}\)What is the solution to g-8= -24?
Answers
Answer:
g=16
Step-by-step explanation:
Answer:
g=-16
Step-by-step explanation:
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive, given that he or she did not have the disease.
The individual actually had the disease
No positive 9 negative 133
Yes
Positive 140
Negative 18
The probability is approximately.
Answers
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
What is probability ?Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.
Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .
Yes No
Positive : 140 9
negative : 18 133
P = \(\frac{Someone get positive }{he not had the disease}\)
= \(\frac{140}{142}\)
=0.985
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
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The price of an item has risen to $196 today. Yesterday it was $80. Find the percentage increase
Answers
So (24% increase I think)
help me with the last one 20 pointsss!!!!
Answers
Answer:
what you need help with? ill help if i can
Step-by-step explanation:
he roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x =
Answers
Stained glass slope graphing linear equation Description: Identify the slope and y-intercept of the linear equation. Then, graph the linear equations on the same coordinate plane. Make sure to extend the lines to the edge of the graph paper! Darken each line when finished. Color however YOU want to create a stained glass effect
Answers
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
What is meant by slope-intercept?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation. Given the slope of the line and the intercept it forms with the y-axis, the slope intercept form in mathematics is one of the forms used to determine the equation of a straight line. Y = mx + b is the slope intercept form, where m is the slope of the straight line and b is the y-intercept.To learn more about slope-intercept, refer to:
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P(x) = x4 – 7x3 + 14x2
+ 14x2 – 3x – 9
Find all real zeros
Answers
Step-by-step explanation:
x4-7x3+14x2-3x-9
This deals with polynomial long division.
Overview
Steps
Topics
Links
1 result(s) found
(x
2
−x−1)⋅(x−3)
2
See steps
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 2 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
((((x4)-(7•(x3)))+(2•7x2))-3x)-9
STEP
2
:
Equation at the end of step
2
:
((((x4) - 7x3) + (2•7x2)) - 3x) - 9
STEP
3
:
Polynomial Roots Calculator :
3.1 Find roots (zeroes) of : F(x) = x4-7x3+14x2-3x-9
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -9.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3 ,9
Let us test ....
I need help I didn't pay attention in class now I am lost.
Answers
In the Ohio lottery Classic Lotto game 6 numbers are drawn at random from 49 possible numbers. What is the probability of your lottery ticket matching all six numbers? Hint: Order is not important.
Answers
The probability of the lottery ticket matching all six numbers is given by
\(\begin{gathered} \frac{1}{49\text{ }}\text{ x }\frac{1}{48}\text{ x }\frac{1}{47}\text{ x }\frac{1}{46}\text{ x}\frac{1}{45}\text{ x }\frac{1}{44} \\ \end{gathered}\)\(\begin{gathered} =\frac{1}{1.006834752\text{ x }10^{10}\text{ }} \\ \end{gathered}\)25 POINTS Simplify the expression. 9 + 2(4 + 10) – 3(6 + 5) answer right and I will give brainiest
Answers
121
Step-by-step explanation:
9+2=11
4+10=14
11×14=154
6+5=11
3×11=33
154-33=121
Answer:
Step-by-step explanation:
9 + 2(14) - 3(11)
9 + 28 - 33
37 - 33 = 4
Select the choice that represents the two-variable
equation after it has been solved for x in terms of y.
2y - 3x = 0
Answers
The two variable equations when solved for x in terms of y is given as the equation y = 3x/2, and option A is the correct answer.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given equation is:
2y - 3x = 0
Add 3x on both sides of the equation:
2y -3x + 3x = 3x
2y = 3x
Divide both sides of the equation with 2:
2y / 2 = 3x / 2
y = 3x/2
Hence, the two variable equations when solved for x in terms of y is given as y = 3x/2, and option A is the correct answer.
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The correct question is:
Help me out with the answer
Answers
Answer:
C i think
Step-by-step explanation:
PLS HELP!!!
WHAT IS THE VOLUME OF THE GIVEN FIGURE
Answers
Answer:
429
Step-by-step explanation:
Answer:
697.08 in³Step-by-step explanation:
This is the combination of two cones with same radius but different heights.
Equation for volume of the cone:
V = 1/3πr²hThe volume of the given figure is:
V = 1/3(3.14)(6²)(5.5 + 13) = 697.08 in³Suppose we have a bottomless bag of 3 different kinds of balls: blue, green, and red. How many possibilities are there to choose 3 balls and arrange them in a line.
Answers
The number of possibilities that are there to choose 3 balls is 6.
How to illustrate the information?From the information, we have a bottomless bag of 3 different kinds of balls: blue, green, and red.
The number of possibilities that are there to choose 3 balls will be:
= 3!
= 3 × 2 × 1
= 6 possibilities.
Therefore, the number of possibilities that are there to choose 3 balls is 6.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Does the series converge or diverge? If it converges, what is the sum? Show your work.
Answers
Step-by-step explanation:
This is a geometric series where our common ratio is -1/2, and a is -4
Since r is less than -1, this series converges so
The sun is
\( \frac{ - 4}{1 + 0.5} \)
\( \frac{ - 4}{1.5} = - \frac{8}{3} \)
The sum is -8)3
Graph the exponential function g (x) = 4* -1
To do this, plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.
Additionally, give the domain and range of the function using interval notation.
Answers
I assume you meant \(g(x)=4^x -1\).
The graph is shown in the attached image.
The two points on the graph are (0,0) and (1, 3).The asymptote is y = -1.The domain is \((-\infty, \infty)\).The range is \((-1, \infty)\).
The two points on the graph are (0,0) and (1, 3).
The asymptote is y = -1.
The domain is (-∞,∞)
The range is (-1,∞)
What is an exponential function?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be written as 2 2 2 2=25 for the number 32. This phrase should be understood as "two to the fifth power."
The two points on the graph are (0,0) and (1, 3).
The asymptote is y = -1.
The domain is (-∞,∞)
The range is (-1,∞)
The graph of the function is attached with the answer.
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help....................
Answers
The unit of the rate of change is (b) dollars per month
How to determine the unit of the rate of changeFrom the question, we have the following parameters that can be used in our computation:
The table of values
Where we have
y = total amount in dollars
x = number of months
The rate of change is calculated as
Rate = y/x
substitute the known values in the above equation, so, we have the following representation
Rate = total amount in dollars/number of months
So, we have
Unit = dollars per month
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please help i will give you a brainly
Answers
Emma bought 7 notebooks for $8.75. How much would 2 notebooks cost?
Answers
Answer:
$2.50
Step-by-step explanation:
8.75 / 7= 1.25
1.25 * 2 =2.50
please please help!! i can’t find anything for this anywhere! :((
find x
Answers
The value of x in the triangle is x=3
In the given triangle a midline passing through the middle iof the triangle makes the triangle in to two triangles.
By midpoint segment theorem
x=1/2(x+3)
Apply distributive property
x=x/2+3/2
Take the variable terms on one side and constant on other side
x-x/2=3/2
x/2=3/2
We get the value of x as three
x=3
Hence, the value of x in the triangle is x=3
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