Integration as the Inverse of Differentiation, Integration of ax" and Integration of the Functions of the Sum or Difference of Algebraic Terms
For each of the following, find f(x).
(a) f'(x) = x³ + 4x -1 1
(b) f'(x) = 1/2x² + root x
(c) f'(x) = 3x - 4 / 2x³
Answers
Answer:
The answer is in the image above
Answer:
Step-by-step explanation:
The antiderivative for b is definitely incorrect, as stated in the comments section.
[tex]\int\limits {\frac{1}{2x^2}+\sqrt{x} } \, dx \\\frac{1}{2} \int\limits{\frac{1}{x^2} } \, dx+\int\limits {x^{\frac{1}{2}} } \, dx[/tex] That's a bit more simplified. One more important simplification and then we can integrate one term at a time:
[tex]\frac{1}{2}\int\limits{x^{-2}} \, dx +\int\limits{x^{\frac{1}{2} } \, dx[/tex] and here we go:
[tex]\frac{1}{2}(\frac{x^{-2+1}}{-2+1})+(\frac{x^{\frac{1}{2}+\frac{2}{2}} }{\frac{1}{2}+\frac{2}{2} })+C[/tex] and
[tex]\frac{1}{2}(\frac{x^{-1}}{-1})+(\frac{x^{\frac{3}{2}} }{\frac{3}{2} })+C[/tex] and finally,
[tex]-\frac{1}{2x}+\frac{2}{3}x^{\frac{3}{2}}+C[/tex]
Related Questions
What is the radius of a circular piece of paper whose circumference is 11
Answers
Answer:
well the circumference is the area of the circle so if you know the diameter then you divide that number by 2
Javier is constructing a door for his son's tree house. The dimensions of the rectangular door are 6a^2-a+2 feet and 3a^2+5 feet. He wants to cut out a square from the door to insert a glass panel, as per the diagram below. The glass panel will have a height of a -3 feet.After Javier removes the square for the glass panel, how much of the door will be made from wood?
Answers
The area of a figure is the amount of space the figure can occupy. [tex]18a^4 + 10[/tex] of the door will be made from the wood.
Given
[tex]Length = 6a^2 + 2[/tex]
[tex]Width = 3a^2 + 5[/tex]
First, calculate the area of the rectangular door
[tex]Area = Length \times Width[/tex]
[tex]Area =(6a^2 + 2) \times ( 3a^2 + 5)[/tex]
[tex]Area = 18a^4 + 6a^2 + 30a^2 + 10[/tex]
[tex]Area = 18a^4 + 36a^2 + 10[/tex]
Next, calculate the area of the glass panel
The dimension of the glass panel is not given, and the diagram is not attached. So, I will assume the dimension of the square glass panel is [tex]6a[/tex].
So, the area of the glass panel is:
[tex]Area = 6a \times 6a[/tex]
[tex]Area = 36a^2[/tex]
To calculate how much wood that will be needed for the rectangular door, we simply subtract the area of the glass panel from the area of the door
[tex]Wood = 18a^4 + 36a^2 + 10 - 36a^2[/tex]
Collect like terms
[tex]Wood = 18a^4 + 10 + 36a^2 - 36a^2[/tex]
[tex]Wood = 18a^4 + 10[/tex]
Considering the assumed value, [tex]18a^4 + 10[/tex] of the door will be made from the wood.
Learn more about areas at:
https://brainly.com/question/16418397
Solve 6x + ( 14x - 5 ) + ( 17 - 3x ) , - ( 2 - x ) -3 ( 6 + 8x ) -12, ( 4x - 9 ) + 8 ( 2x + 3 ) -7x
Answers
Answer:
Step-by-step explanation:
6x + ( 14x - 5 ) + ( 17 - 3x )
= 17x + 12
- ( 2 - x ) -3 ( 6 + 8x ) -12,
= -23x - 32
( 4x - 9 ) + 8 ( 2x + 3 ) -7x
= 13x +15
What time is shown on the clock
Answers
Answer:
9:18
Hope this helps <3
find the value of x and y
Answers
Answer:
x=11
y=3
Step-by-step explanation:
(9x+25)=(13x-19)
9x+25 = 13x−19
9x+25-25 = 13x−19-25
9x=13x-44
9x-13x=13x-44-13x
-4x= -44
x=11
y= 180-(9x+25)
y= 180-(99+25)
y= 180-124 = 56
y= 56-5 = 51
y= 51/17
y= 3
Good luck
-5r - 3r = ?
Can someone explain how to do solve this?
Answers
Answer:
-8r
Step-by-step explanation:
-5r - 3r
Combine like terms
Factor out r
r( -5-3)
-8r
Answer:
like bases combine under add/subtract
-5 minus 3 is -8
-8r would be the solution
Step-by-step explanation:
is a rectangle. EA is 12 in. Find the length of the diagonal .
12 in.
24 in.
6 in.
26 in.
Answers
Answer:
hey please saw the figure
Answer:
Step-by-step explanation:
its 24
Which names are other ways to name _1? Select each correct answer.
y
pfy
pyf
p
yfp
ypf
f
Answers
Answer:
your answer is F
I hope it's helps you
What is the value of U. 51degrees, 79degrees and u.
Answers
Hi ;-)
[tex]u+51^o=79^o\\\\u=79^o-51^o\\\\\huge\boxed{u=28^o}[/tex]
The required equation is,
→ 51° + U = 79°
Now we should,
find the required value of U.
→ 51° + U = 79°
→ U = 79° - 51°
→ [U = 28°]
Let's check whether the required value of U is correct or incorrect,
→ 51° + U = 79°
→ 51° + 28° = 79°
→ 79° = 79°
→ LHS = RHS
Hence, 28° is the required value of U.
5. You want to have a pizza party this weekend for some friends and family. You have $48
budgeted for the pizza and plan on having 56 pieces available. A large pizza has 16 pieces and
costs $14. A medium pizza has 12 pieces and costs $10. How many large and medium pizzas do
you need to buy?
Answers
Ele:
2.
Find the sum of the digits of each multiple of 9 below.
Sum of digits
9
1 + 8 = 9
9.1 = 9
9.2 = 18
9.3 = 27
9.4 = 36
9.5 = 45
9.6 = 54
9.7 = 63
9.8 = 72
9.9 = 81
Describe a pattern. (Do you think it will continue?)
Answers
Answer:
The pattern is that, every time a 9 is added. This pattern continuous forever.
Step-by-step explanation:
9 X 1 = 9
9 X 2 = 18 (9+9)
9 X 3 = 27 (9+9+9)
Etc.
What is the coefficient
Answers
Answer:
B
Step-by-step explanation:
Using the Pascal's triangle
Pertaining to the 8th term the coefficients are;
1, 8, 28, 56, 70, 56,28, 8 and 1 in that order
Expanding this,
the coefficient of the term x^7y is 8
Find the largest integer that is below Square root 10
Answers
Answer:
3.16
Step-by-step explanation:
The pie chart represents the results of an online poll question, Should cell phones be banned in schools?. A total of 1840 girls were asked the question, with 379 answering yes and 1461 girls answering no. The larger section of the pie is labeled as no, representing the count of 1461 girls who answered as no and the smaller section is labeled as yes, representing the count of 379 girls who answered as yes. What percent of girls who voted in this poll think that cell phones should be banned from schools? Give your answer as a whole number.
Answers
a b and c lie on a straight line given that angle y = 125 and angle z = 313 work out x
Answers
Answer:
∠x = 78
Step-by-step explanation:
∠y + ∠1 = 180
=> 125 + ∠1 = 180
=> ∠1 = 180 - 125
=> ∠1 = 55
∠z + ∠2 = 360
=> 313 + ∠2 = 360
=> ∠2 = 360-313
=> ∠2 = 47
∠1 + ∠2 + ∠x = 180
=> 55 + 47 + ∠x = 180
=> ∠x = 180 - 55 - 47
=> ∠x = 78
Answer:
[tex]x=78[/tex]
Step-by-step explanation:
Skills needed: Exterior Angle Theorem, Triangle Geometry:
1) We need to solve for [tex]x[/tex] and there are 2 methods to do it. I will go over the fastest way (since it's better).
This involves the exterior angle theorem (see the image attached to see how that works.2) In order to use this theorem, we need to solve for the angle near [tex]z[/tex]. This angle would be [tex]360-z[/tex], which is [tex]360-313[/tex] (since [tex]z=313[/tex]).
[tex]360-313[/tex] = [tex]47[/tex]
3) Then, we can use the fact that [tex]y=x+47[/tex] (47 is the measure of the angle we just solved for.)
[tex]y=125[/tex], so [tex]125=x+47[/tex]
Subtract 47 from both sides, and get [tex]x=78[/tex]
Hope you understood and have a nice day! :D
Note: I have attached one image that shows my work, and another image that shows the exterior angle theorem (which I created on a whiteboard). Hope you get it! If you have any questions, comment and I can answer it ASAP!
2x-ky=14 and 5x-2y=5
In the system above, k is a constant and x and y are variables For what values of k will the system of equations have no solution.
Answers
Answer:
Step-by-step explanation
In these type of questions we can use a trick to find answer
let's say we have two linear equation
1) ax+by+c=0
2)mx+ny+t=0
if a/m = b/e ≠ c/f that means we don't have any solution for these two equations ( that's because of analitic geometry)
so,
2x-ky-14=0
5x-2y-5=0
2/5=k/2≠14/5 k=5If k is 4/5, the system of equations will have no solution because the lines are parallel.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system will have no solution if the two equations represent parallel lines, because parallel lines do not intersect.
To determine if the lines are parallel, we can compare the slopes of the two lines.
The slope of the first line is 2, since it is the coefficient of x when we solve for y:
2x - ky = 14
ky = 2x - 14
y = (2/k)x - 14/k
The slope of the second line is 5/2, since it is the coefficient of x when we solve for y:
5x - 2y = 5
2y = 5x - 5
y = (5/2)x - 5/2
Therefore, the two lines are parallel if the slopes are equal:
2/k = 5/2
4 = 5k
k = 4/5
So, if k = 4/5, the system of equations will have no solution because the lines are parallel.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Kay's mother's age is six more years than twice Kay's age. The sum of their ages
is 81. Find both of their ages.
Answers
Answer:
6x81=2
Step-by-step explanation:
What is 5 x 0.1 + 4 x 0.01 + 8 x 0.001 written in standard form?
Answers
Answer:
0.548
Step-by-step explanation:
5 x 0.1 = 0.5
4 x 0.01 = 0.04
8 x0.0001 = 0.008
Now add them all together to get 0.548 in standard form.
I hope this helps! :)
Answer:
5 × 0.1 is 0.5
4 × 0.001 is 0.04
8 × 0.0001 is 0.008
so add all number is
0.548
4. Find the quotient. -7 ÷ 14/3
Answers
As a mixed number, this is -1 and 1/2
As a decimal this is -1.5
-3/2
As a mixed number this is -1 1/2
as a decimal this is - 1.5
(x-1)^2+(2-x)^2-3(x-5)*(x-5)
Answers
Answer:
[tex]-x^2+24x-70[/tex]
Step-by-step explanation:
[tex](x-1)^2+(2-x)^2-3(x-5)*(x-5)\\=> (x - 1)^2 + (2 - x)^2 - 3(x - 5)^2\\=> x^2 - 2x + 1 + 4 - 4x + x^2 - 3(x - 5)^2\\=> x^2 - 2x + 5 - 4x + x^2 - 3(x - 5)^2\\=> x^2 - 6x + 5 + x^2 - 3(x - 5)^2\\=> 2x^2 - 6x+5 - 3(x - 5)^2\\=> 2x^2 - 6x+5 - 3(x^2 - 10x + 25)\\=> 2x^2 - 6x+5 - 3x^2+30x-75\\=> -x^2 - 6x + 5 + 30x - 75\\=> -x^2 + 24x + 5-75\\=> -x^2+24x-70[/tex]
Formula used =
[tex](a-b)^2 = a^2+ 2ab + b^2[/tex]
HELP ASAP HOMEWORK HELPPPP
Answers
What is 234 (two hundred and thirty four) X 0.35?
Answers
Answer:
81.9
Step-by-step explanation:
mark me brainliest plzz
234(234)×0.3
234×234×0.3
54,756×0.3
16,426.8
what is a example of the reflexive property.
Answers
Answer: 3 is equal to 3
Explaination: We all have learned that reflexive property of equality means that anything is equal to itself. So, this property tells us that anything is equal to itself.
Explain how to do order of operations. Use an example
Answers
Answer:
First, solve what is in the parentheses of the function. Next, solve the exponents. This includes normal exponents, negative exponents, square roots, cube roots, etc. After that, multiply and divide, and finally, add and subtract the remaining equation.
0.6m=____mm . answer the question
Answers
Answer:
600
Step-by-step explanation:
since 1m=1000mm
If you need an explanation how ill explain in the comments
I need help solving this.
16 - 2t + 5t +9
Answers
Answer:
give brainliest please I need it to level up
Step-by-step explanation:
16 - 2t + 5t + 9
16 + 9 -2t + 5t=0
25 + 3t =0
3t= -25
t= -8.3
A sailboat travels a distance of miles in of an hour. Which complex fraction represents the unit rate in miles per hour?
Answers
Answer: I think its D and A
Step-by-step explanation:
Answer:
im pretty sure its D and also A
Step-by-step explanation:
Please help me I will mark brainliest :)
Answers
Answer:
X should equal 12.
Step-by-step explanation:
I say this because we know TED= 30° bc 50°-20° = 30
then u have to think about what × 2 + 6 equals 30
sure enough 12 × 2 = 24 and 24 + 6 = 30
that's why I say X equals 12
Estimate the shaded areas of the following shapes.???
Answers
Answer:
436cm^2
Step-by-step explanation:
you're gonna have to round up to the nearest whole number.for no.2 split the shape so that it'll give u two rectangles.for no.3 find the area of the small rectangle and minus from the area of the big rectangle
Big rectangle =30*16=480
small rectangle =4*11=44
480-44=436
please help me with this and explain your answer
Answers
Answer:
B
Step-by-step explanation:
t=4x+c
Since we are looking for x,
t-c=4x
Divide through by the coefficient of x which is 4
4x/4=t-c/4
Therefore, x=t-c/4
