True or False.
If

F(x) = ∫ -23x sin(t) dt

then the second fundamental theorem of calculus can be used to evaluate F '(x) as follows

F '(x) = sin (3x)

Answers

Answer 1

Answer:

False.

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Integration

IntegralsDefinite IntegralsIntegration Constant C

Integration Rule [Fundamental Theorem of Calculus 2]:                                     [tex]\displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle F(x) = \int\limits^{3x}_{-2} {sin(t)} \, dt[/tex]

Step 2: Differentiate

Chain Rule:                                                                                                     [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot \frac{d}{dx}[3x][/tex]Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot 3\frac{d}{dx}[x][/tex]Basic Power Rule:                                                                                         [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot 3x^{1 - 1}[/tex]Simplify:                                                                                                         [tex]\displaystyle F'(x) = 3\frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt][/tex]Integration Rule [Fundamental Theorem of Calculus 2]:                           [tex]\displaystyle F'(x) = 3sin(3x)[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e


Related Questions

Change each decimal to a percent by moving the decimal point two places
to the right. 0.762

Answers

literally 76.2%. doesn't it say it in the text...

Answer:

76.2%

Step-by-step explanation:

uhm please help me
I’m not really good at Math as you can tell :(

Also: Don’t mind the tabs (^^;)

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Answer:

5 37.50

10 75

hope it helps

Step-by-step explanation:

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Lol the you tube tab though XD

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Answer:

Step-by-step explanation:

a = 1935 / 5 is the change

b = 1960 / 10 is the change

c = 1950 / 20 is the change

They are all increasing i'd assume they all went threw a positive change

(Find the GCF of the set of monomials) and if you can help with the other four that would be greatly appreciated
75,27 the GCF =

Answers

Answer:

ба ман нуқтаҳо лозиманд :) умедворам шумо мефаҳмед

Step-by-step explanation:

Answer:

What is the GCF of 75 and 27? The GCF of 75 and 27 is 3.

Step-by-step explanation:

Solve for x. show work. 8+b/-4=5

Answers

Answer:

b=12

Step-by-step explanation:

What's at stake?

Forests are cradles of life—around four-fifths of all land species live in tropical forests. They play a vital role in regulating our climate by absorbing carbon dioxide, and help maintain our soil and water.

Forests directly support around 1.6 billion people—nearly a quarter of the world's population. And we all rely on them for the air we breathe and the countless products they provide.

But over the last half-century, people have destroyed forests at an alarming rate. We've already lost around half of the world's original forests.


The story so far

In the early 1990s, we campaigned to stop the timber industry destroying and degrading the world's forests.

At the time, few businesses believed they were responsible for where their timber came from. Those that did claim to sell products from well-managed forests had no way of proving it.

"Businesses didn't think the environment was their concern," recalls Jean-Paul Jeanrenaud, who led WWF-UK's work on forests at the time.

"We had chief executives slamming the phone down on us. I even had people threaten to punch me."

How things have changed… In September 1991, British DIY chain B&Q committed to working with us to buy only legal, sustainable timber. By the end of that year, 16 large UK companies had committed to sourcing their timber products from well-managed forests.

That was the beginning of our Global Forest & Trade Network. Today, it's a global partnership of some 275 retailers, producers, community groups and other organizations from across the forest industry supply chain. Members are committed to safeguarding the world's forests and the communities, economies and ecosystems that depend on them.

But we needed a way to turn those commitments into reality. So in 1993, we helped form the Forest Stewardship Council (FSC) to certify timber and wood-based products that meet high environmental and social standards.

For a forest to be FSC certified, independent inspectors check that it meets the FSC's strict criteria. All trees that are cut down have to be replaced or allowed to re-grow naturally, and parts of the forest are left untouched. The rights of indigenous people are respected, and local workers are employed on a decent salary. Often, companies support other social services, such as schools and clinics.

Inspectors also check every stage along the supply chain, so you can be sure that any product that bears the FSC logo is good for forests, people and wildlife.


Did you know?

Just 10 years ago, only 300 sq km of forest in Russia was FSC-certified. Today, it's 260,000 sq km—a quarter of its commercial forests.


Facts and stats

1.4 million sq km—area of forest certified by the FSC. That's an area more than twice the size of France
81—number of countries with FSC-certified forests
40 percent—forest area of Europe and North America certified by the FSC
US$73bn—annual sales of forest-based products by members of our Global Forest & Trade Network

What next?

Almost a tenth of forest products traded now meet FSC standards. That's a phenomenal rate of growth—but it means nine-tenths of products are still uncertified.

We believe some areas of forest need to be protected from any commercial logging. But we're supporting responsible forestry alongside protected areas to help conserve the world's most important forests:

In the Congo Basin, the largest area of tropical forest after the Amazon, 45,000 sq km is now FSC certified—and we're working with everyone from heads of state on down to increase this. As well as protecting important habitats for elephants, great apes and many other species, sustainable forestry is improving livelihoods for some of the poorest people on the planet.
In Borneo, we're working to conserve and restore the "Heart of Borneo," a 220,000 sq km area of the island's species-rich rainforest. Responsible forestry is a vital aspect of this: some 20,000 sq km is already FSC certified or in the process of certification. By 2020, we want the entire Heart of Borneo area to be protected or managed sustainably.
In the western Mediterranean, people have sustainably harvested cork for centuries. Cork oak forests provide a haven for rare plants, birds and other wildlife, including the Iberian lynx, the world's most endangered wild cat. We're promoting FSC certification to keep sustainable cork harvesting economically viable and help protect this unique landscape.

What you can do

You can help secure a future for the world's forests, and the people and animals that depend upon them next time you buy a table—or any other wood-based product.

Only buy products with the FSC label—it's the only credible certification scheme.

If you don't see the logo, ask the store or manufacturer why not. Make sure they realize that you as a customer want to know that the products you buy don't destroy forests. This message will swiftly get back to their suppliers.

Answers

Answer:

a type of meat that you can eat

Car survey
In a survey of 2400 people who owned a current type of car, 1440 said they would buy that type of car again.....

Answers

Answer: 60%

Step-by-step explanation:

1440/2400

Divide both numbers by 480

The quotient is now:

3/5

To find the percentage of a fraction of people, you have to multiply the fraction by 100%

3/5 x 100% = 300/5

300/5 = 60%

Answer:

its 20

Step-by-step explanation:

Isaac walks 6/10 of a mile of a mile in 1/5 of an hour. If Isaac’s walking rate remains constant, what is Isaacs walking rate in miles per hour?

Answers

Answer:

3 miles per hour.

Step-by-step explanation:

To get his walking rate in miles per hour, we multiply 1/5 by its reciprocal, 5/1. We also multiply 6/10 by 5/1. This gets us 30/10 of a mile in an hour. We can simplify 30/10 to 3. This means he walks at 3 miles per hour.

PLZZZHELP
ill mark brainliest

Answers

Answer:

[tex]y=\frac{x+2}{4}[/tex] or y = 0.25x + 0.5

Step-by-step explanation:

You need to try change the subject from x to y.

x = 4y - 2

We first move -2 to the left, making the equation

x + 2 = 4y i.e.

4y = x + 2

We then divide both sides by 4.

[tex]y=\frac{x+2}{4}[/tex] or y = 0.25x + 0.5

We now have successfully made y the subject, and effectively solving the equation.

whats the relation ship between these two

Answers

i think it’s c.
:) bddffzz
Im not sure if it’s only me , but the image won’t load for me

but other than that have an amazing day !

HELPPPPpPpPPP BRAINLIESTTTTTT

Choose the inequality that matches the verbal description.

The number of girls in Mrs. Baugh's homeroom is greater than 8.

A) x ≤ 8

B) x ≥ 8

C) x > 8

D) x < 8

Group of answer choices

A

B

C

D

Answers

It’s “C” :))))))))))))$

Answer:

The correct answer is C

Step-by-step explanation:

because

A). would be x Less than or equal to 8

B). would be x Greater than or equal to 8

C). would be x Greater than 8

D). would be x Less than 8

Can you please help me:)​

Answers

9514 1404 393

Answer:

  (Bashir) x +29; (Deb) x -5

Step-by-step explanation:

We are told that ...

  Jin raised x dollars

  Bashir raised $29 more, so (x +29).

  Deb raised $34 less than Bashir, so (x+29)-34 = (x -5).

Seven less than three times a number is 14. Find the number.

Answers

Answer:

Steps:

Use the equation 3x-7=14 to find the missing number.

Add 7 to both sides.

3x=21

Divide both sides to isolate x

x=7

Therefore, the correct answer is 7.

You can check by multiplying 7 by three and then subtracting 7 from it and get 14.

Do you like my drawing

Answers

Answer:

yes!!!

Step-by-step explanation:

Answer: yes I like it

Step-by-step explanation:

Please help!
Y=____x+____

Answers

Answer:

Y = 3/4x + -5

___________

y = 3/4x – 5

Step-by-step explanation:

y = mx + b

m = slope = change in y/change in x = rise / run

b = y intercept = point where x = 0

Maya is going to watch a movie in her collection. She has 3 action movies, 11 comedies, and 9 dramas. She will randomly select one movie. What is the probability that the movie she selects is not a comedy?

Answers

Answer:

The probability is 12/23

Step-by-step explanation:

We calculate the number of movies in her selection

Mathematically, that will be;

3 + 11 + 9 = 23

The number of movies that are not comedy will be;

3 + 9 = 12

So the probability of selecting a movie that is not comedy will be 12/23

In a bag, you have a strip of paper with the numbers 1-10 written on the strips. If one strip of paper is pulled from the bag and then replaced, what is the probability of the following events:
pick a odd number and then a even number.

A: 1/2
B: 1/4
C: 1/5
D: 1/25

Answers

I’m stuck on c or b buttttt my best guess is c tell me if this helped :)

What is the solution to the system of equations graphed below?
y = 2x - 7
y = -x-1
A. (4,1)
B. (3,-2)
C. (0, -1)
O D. (2,-3)

Please help

Answers

Answer:

(2,-3) thats where they intersect

and also that the answer

Step-by-step explanation:

11
0/1
DF bisects LCDE. Find the value of x.
E
8x
D
(4x +30)

Answers

cant help on this one. sorry. try 10 tho

7 + 24 .3
31
55
c
96
112

Answers

Answer:

The answer is 325.3

Step-by-step explanation:

I hope this helped I used a calculator sorry if I'm late and I hope this isn't wrong

Solve for x and find AB
Solve for y and find BX

Answers

9514 1404 393

Answer:

x = 7; AB = 30y = 5; BX = 25

Step-by-step explanation:

Opposite sides of a parallelogram are the same length.

  AB = CD

  5x -5 = 3x +9

  2x = 14

  x = 7

  AB = 5(7) -5)

  AB = 30

__

The diagonals of a parallelogram are bisected by each other.

  XB = XD

  7y -10 = 5y

  2y = 10

  y = 5

  BX = 7(5) -10

  BX = 25

20 points. A triangle has an exterior angle with a measure of 120°. Can you determine the measures of the interior angles?

The answer is no, I just need an explanation why, thank you :)

Answers

Answer:

Step-by-step explanation:

it is no because there is only 1 angel that u have

Explain ASAP PLEASE!!!!!!

Answers

Answer:

C

Step-by-step explanation:

you can make a right triangle from the center of one base to the edge of that circle, and then up to a point on the circumference of the other base

the bases of the triangle would be 2 and 5

so that gives sqrrt 29

Sally was painting an airplane on a canvas using a 1in.: 8ft scale. If her painting was 29 inches wide, what was the actual width of the airplane?

Answers

Answer:

232 inches or 19.33 feet

Step-by-step explanation:

232 feet is the  actual width of the airplane.

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Sally was painting an airplane on a canvas using a 1in.: 8ft scale

1 inches = 8 ft scale.

Sally painting was 29 inches wide.

We have to find the actual width of the airplane.

Convert 29 inches to feet.

As we know 1 inche is 8 feet so 8 inches will be the multiple of 8 and 28.

29×8

232 feet.

Hence, 232 feet is the  actual width of the airplane.

To learn more on Unit of Measurement click:

https://brainly.com/question/15402847

#SPJ5

May you please help me with this question!

Answers

Answer:

9/4x to the power of one plus 12y to the power of one

Step-by-step explanation:

You can add the top numbers for 9, but cant add the bottoms since they are different variables.

Answer:

[tex]\frac{6y+7x}{12xy}[/tex]

Step-by-step explanation:

i hope this helps :)

Which expression uses the associative property to make it easier to evaluate 14(1/7x2/5)?
A. (14x1/7)2/5
B.7(1/14x2/5)
C.(14x5/2)1/7.
D.14(2/5x1/7)​

Answers

Answer:

A

Step-by-step explanation:

Associative property:

(a+b)+c=a+(b+c)

(a*b)*c=a*(b*c)

Can someone help me! Please

Answers

Answer:

4c - 2

Step-by-step explanation:

Add up all the terms to find the perimeter.

2c + 2(c - 1)

2c + 2c - 2

4c - 2

Therefore, the perimeter is 4c - 2.

Figure ABCD was reflected across the x-axis to create
figure A'B'CD!
What are the coordinates of the pre-image of B'?
(2,-8)
(-8,-2)
(-2, 8)
(8, 2)

Answers

Answer:

I think the answer is (8,2)

Which issue is among those addressed by Articles VII–VIII?

constitutional amendments
elections
separation of powers
taxation

Answers

Answer:

C

Step-by-step explanation:

Answer:

c <3

Step-by-step explanation:

have a blessed day <3

Jamaican sprinter Usain Bolt 100 m sprint gold medal in the 2012 Summer Olympics Iran the hundred meter race and 9.63 seconds there are about 3.28 feet in a meter and 5280 feet in a mile what was used on Ballz average speed for the hundred meter race in miles per hour

Answers

Answer: 23.2 miles per hour

Step-by-step explanation:

He ran 100 meters in 9.63 seconds.

First convert the number of meters he ran to miles:

= 100 * 3.28

= 328 feet

= 328/5,280

= 0.062121212 miles

Convert the seconds to hours:

= 9.63 / 60

= ‭0.1605‬ minutes

= ‭0.1605‬/60

= ‭0.002675‬ hours

Speed in miles per hour is:

=  0.062121212 / ‭0.002675

= 23.22

= 23.2 miles per hour

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