Use the Fundamental Theorem of Calculus to find the "area under curve" of
f
(
x
)
=
6
x
+
19
between
x
=
12
and
x
=
15
.

Answers

Answer 1

Answer:

[tex]\displaystyle A = 300[/tex]

General Formulas and Concepts:

Calculus

Integrals

Definite IntegralsArea under the curveIntegration Constant C

Integration Rule [Reverse Power Rule]:                                                                   [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/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]

Area of a Region Formula:                                                                                       [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 6x + 19

Interval [12, 15]

Step 2: Find Area

Substitute in variables [Area of a Region Formula]:                                       [tex]\displaystyle A = \int\limits^{15}_{12} {(6x + 19)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]:                   [tex]\displaystyle A = \int\limits^{15}_{12} {6x} \, dx + \int\limits^{15}_{12} {19} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:                   [tex]\displaystyle A = 6\int\limits^{15}_{12} {x} \, dx + 19\int\limits^{15}_{12} {} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]:                      [tex]\displaystyle A = 6(\frac{x^2}{2}) \bigg| \limits^{15}_{12} + 19(x) \bigg| \limits^{15}_{12}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:              [tex]\displaystyle A = 6(\frac{81}{2}) + 19(3)[/tex]Simplify:                                                                                                             [tex]\displaystyle A = 300[/tex]

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

Unit: Integration

Book: College Calculus 10e


Related Questions

Examine the system of equations.

y = negative one-fourth x minus 2

x = 4

What is the solution to the system?
(–3, –2)
(4, –3)
(4, –2)
(4, –1)

Answers

The answer is 4,-3

Irfcdxsaacd d

Answer:

4,-3

Step-by-step explanation:

Divya is painting a room. She uses 34 gallon of paint to cover 15 of a wall. If the walls are all the same size, how much paint will she need to cover one wall?

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She will need 15 gallons

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The reason I plugged 4 into the y spot of the equation and -2 into the x spot is because it allows us to find where the y intercept is if we solve for it. Look at picture for work and answer. Hope this helps.

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Answers

Answer:

t = 4 or t = -16

Step-by-step explanation:

Let's solve your equation step-by-step.

2+|t+6|=12

|t+6|+2=12

Step 1: Add -2 to both sides.

|t+6|+2+−2=12+−2

|t+6|=10

Step 2: Solve Absolute Value.

|t+6|=10

We know eithert+6=10 or t+6=−10

t+6=10(Possibility 1)

t+6−6=10−6(Subtract 6 from both sides)

t=4

t+6=−10(Possibility 2)

t+6−6=−10−6(Subtract 6 from both sides)

t=−16

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Answer:

the national league

Step-by-step explanation:

evaluate -(2^-6)(2^3)

Answers

Answer:

-0.125

Step-by-step explanation:

Just had that question on SAT

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Step-by-step explanation:

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Answers

Answer:

I think they are SAS but I'm not sure

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You have to get a calculator online

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Answers

Answer:

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Step-by-step explanation.

125 x 8 = 1000

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Answers

Answer:

-4 5/12

Step-by-step explanation:

-2 3/4 - 1 2/3

3/4*3/3= 9/12    2/3*4/4= 8/12

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Answers

Answer:

Answer is 20

Step-by-step explanation:

4-4(-4) is = 20!

Please mark me Brainliest!

Can u also help me with the question I just posted?

3 bananas cost $0.33. At this rate, how much do 5 bananas cost?

Answers

0.33/3 = 0.11
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Wich equation best represents the relationship between x and y in the graph?

Answers

Answer:

sorry for wasting your time

need pionts

Answer:

y=3x+3

How I got it:

from the graph, you can tell that the slope is 3/1, or 3 by counting up 3 on a point, then over 1.

Slope = 3

then you can tell the y intercept is 3 by.. well looking at where the line intercepts the y axis.

Y intercept = 3

the slope-intercept formula is:

y=mx+b

m being the slope, b being the y intercept. now you just plug in what you know!

y=3x+3, which is the answer

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Answers

Answer:

16

Step-by-step explanation:

The answer is 1”16 ur welcome

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Answer:

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Step-by-step explanation:

What is the solution to the system of equations graphed below

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Answers

The answer will be (2,-3) it’s 2 to the right and 3 down.

Answer: The answer will be (2,-3) it’s 2 to the right and 3 down.

Step-by-step explanation: yay

A recipe uses 4 cups of milk to make 12 servings. If the same amount of milk is used for each serving, how many servings can be made from three gallons? Before you try that problem, answer the question below. How many cups will you need to find the number of servings for?

Answers

Answer:

144 servings

Step-by-step explanation:

Step 1

We convert 3 gallons to cups

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x = 3 × 16 cups

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Step 2

If

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x = 48 × 12/4

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Answer:

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Step-by-step explanation:

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Answers

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1 only has a single factor which is 1, so you can't really say.

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Shelley reaches into a bag of candies and chooses one without peaking. 1 point
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Answer:

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Answers

Answer:

2

Step-by-step explanation:

550 / 6 = 91 with a remainder of 4. They need 2 more to get to the required 6.

The number of sheets of paper the class need to make one more cube is 2.

Given that, a class makes origami cubes. Each cube requires 6 sheets of paper.

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The class makes as many cubes as possible with 550 sheets of paper.

Here, 550/6

6|550|91

  54
_____

    10

    6
_____

    4

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Answers

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Step-by-step explanation:

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Answers

Answer:

A significant correlation means that there is a significant (in a statistical point of view) correlation between two things.

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Which statement BEST describes how muscles respond to weight training? A. Weight training stretches the muscles' limits and makes the muscles longer. B. Weight training pushes the muscles' abilities, making the muscles gain endurance. C. Weight training stimulates the muscles and causes the muscle fibers to sit closer together. D. Weight training overloads muscles, which causes the body to respond by making muscle fibers larger. Please select the best answer from the choices provided. A B C D

Answers

Answer:B

Step-by-step explanation:

The statement that best describes how muscles respond to weight training is:

Weight training overloads muscles, which causes the body to respond by making muscle fibers larger.

Option D is the correct answer.

What is weight training?

Weight training, also known as resistance training, involves performing exercises that place a load or resistance on the muscles.

This load creates small tears or damage to the muscle fibers, which the body then repairs and adapts to by making the muscle fibers larger and stronger.

We have,

Option A:

Weight training stretches the muscles' limits and makes the muscles longer, which is not an accurate description of how muscles respond to weight training.

While stretching exercises can increase muscle flexibility, weight training typically does not cause the muscles to become longer.

Option B

Weight training pushes the muscles' abilities, making the muscles gain endurance, which is partially true.

Weight training can increase muscle endurance by strengthening the muscles, but the primary response of the muscles to weight training is hypertrophy, not increased endurance.

Option C:

Weight training stimulates the muscles and causes the muscle fibers to sit closer together, which is not an accurate description of how muscles respond to weight training.

While weight training does stimulate the muscles, it does not cause the muscle fibers to sit closer together.

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Answers

Answer:

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Step-by-step explanation:

18 letters and 8 bills

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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6
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h =
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

-80

Step-by-step explanation:

First you multiply both sides of the equation by 5 to get rid of the fraction, it becomes Y + 30 = -50.

To get rid of the 30 you subtract 30 from each side and that makes it Y = -80.

Your answer does not want the Y=, so your answer is -80.

If this helps, please mark it Brainliest :)

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