need to evaluate integral pls help me

Need To Evaluate Integral Pls Help Me

Answers

Answer 1

Answer:

[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]

General Formulas and Concepts:

Calculus

Integration

IntegralsIntegral Notation

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]

Integration Property [Splitting Integral]:                                                               [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.[/tex]

[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?[/tex]

Step 2: Integrate

[Integral] Rewrite [Integration Property - Splitting Integral]:                       [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {f(x)} \, dx + \int\limits^2_1 {f(x)} \, dx[/tex][Integrand] Substitute in function:                                                               [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {9x^9} \, dx + \int\limits^2_1 {4x^3} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:               [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \int\limits^1_0 {x^9} \, dx + 4 \int\limits^2_1 {x^3} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]:                                    [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{x^{10}}{10} \bigg) \bigg| \limits^1_0 + 4 \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^2_1[/tex]Integration Rule [Fundamental Theorem of Calculus 1]:                            [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{1}{10} \bigg) + 4 \bigg( \frac{15}{4} \bigg)[/tex]Simplify:                                                                                                         [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]

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

Unit: Integration

Answer 2

Answer:

Step-by-step explanation:

[tex]\int\limits^1_0 {9x^9} \, dx +\int\limits^2_1 {4x^3} \, dx[/tex]

=[tex]\frac{9x^{10}}{10} |_0^1 + x^4|_1^2[/tex]

[tex]=\frac{9}{10}+2^4 -1 = 15\frac{9}{10}[/tex]


Related Questions


Sara says, "If you subtract 17 from my number and multiply the difference by - 4, the result is
- 60." What is Sara's number?

Answers

Answer:

32

Step-by-step explanation:

ok to the result is - 60 she said. So then we know that in order to get -60, you had to subtract 17 from the original number and multiply by -4.

equation is this: (x-17)×-4= -60

Next, we solve using pemdas!

x-17=[tex]\frac{-60}{-4}[/tex]   (keep in mind that a negative cancels out a negative!)

add 17 to both sides

x= [tex]\frac{-60}{-4}[/tex]+17

So then now that you have the new equation you simplify!

x= 32

Help help math math math

Answers

Answer:

This is a nonlinear function

Step-by-step explanation:

This is because in increase in y changes every time in this function, from 3 to 5 to 7

The answer is Non-Linear. Hope this helps :)

For the following inequality, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the inequality. Be sure to include at least two terms from the word bank
1/4 x \leq -3

Answers

Answer:

x<=-12

Step-by-step explanation:

1/4x<=-3

*Multiply both sides by 4

x<=-12

and it's solved :)

Ivanna drove 420 miles using 18 gallons of gas. At this rate, how many gallons of gas would she need to drive 357 miles?

Answers

Answer:

15.3 GAL.

Step-by-step explanation:

(x+1)/(x+2)=3/4
Solve the equation​

Answers

4(x+1)=3(x+2)

4x+4=3x+6

4x-3x=6-4

X=6-4

Answer is X=2

Evaluate 40x40x402x2x2

Answers

Answer:

2,572,800

Step-by-step explanation:

I hope this helps!

Answer: 40 x 40 x 402 x 2 x 2 =128,640

What is the sales tax on a jacket priced at $275 if the sales tax rate is 7%?

Answers

the answer is 19.25, because when you ..

For this item, complete the choice matrix by clicking the appropriate answer in each row.
Determine whether each unit rate is equivalent or not equivalent to
Equivalent
Not Equivalent
the unit rate, in inches per year, of growing inch in Ğ of a year
the unit rate, in lessons per hour, of finishing of a lesson in hours
the unit rate, in miles per hour, of jogging 1/8 mile in 3/8 hour

Answers

Step-by-step explanation:

1/2 inch in 2/3 of a year

1/2 / 2/3 = 1/2 × 3/2 = 3/4

NOT equivalent.

4/9 lesson in 4/3 of an hour

4/9 / 4/3 = 4/9 × 3/4 = 12/36 = 1/3

Equivalent.

1/8 mile in 3/8 of an hour.

1/8 / 3/8 = 1/8 × 8/3 = 8/24 = 1/3

Equivalent.

A basketball player made 80 out of 100 attempted free throws what percent of free throws was made ?

Answers

Answer:

8/10

Step-by-step explanation:

id hope your have a great day

Answer:

80%

Step-by-step explanation:

80÷100=.8 which is 80%

Which choice is equivalent to the product below?
14.6
O A. 125
B. 6-28
C. 2-21
D. 28

Answers

Answer:

2√21

Step-by-step explanation:

1) Simplify.

√84

2) Simplify √84 to 2√21.

2√21

Number 1. What is 42% of 80

Answers

Answer:

The answer is 33.6.

Hope that helps?

Step-by-step explanation:

Worth 50 points!I need help plz!
Will mark brainliest to whoever does all the work.

A basket contains:
4 red Santa hats
6 green Elf hats
5 red jackets
7 green jackets.

Determine the probability of randomly selecting a green piece of clothing or a jacket.

(A)Use the addition rule to calculate this probability and explain your answer.

Do this equation P(AorB)=P(A)+P(B)-P(A and B)
(Write your answer as a percent.)

(B) are a green piece of clothing and a jacket mutually exclusive events?

Answers

Explanation/Answer:

Total: 4 + 6 + 5 + 7 = 22

Green: 6 + 7 = 13

Probability: 13/22

Note: It Is Not Mutually Exclusive Events

I need the anwser to this right now please

Answers

Answer:

b. 9

Step-by-step explanation:

2+9=11

11+11=22

22+6=28

answer: 9

(3+3)-28 = 22
that leaves the other side having to be 11 on each so
2+9= 11

The values in the five-number summary divide a data set into four quarters.
A. True
B. False

Answers

Answer:

The values in the five-number summary divide a data set into four quarters.

→ True

Mark me as brainlist plz :)

Answer:

the answer is TRUE

Step-by-step explanation:

Please look for the question in the picture.

Answers

Answer:

I beleive the missing value is -3

Step-by-step explanation:

if you plug -3 into the pink box it will give you the result of -5

(anyone is free to correct me)

I SWEAR IF I GET ANOTHER LINK I WILL SCREAM Parth created a Box-and-Whisker Plot to show the average weight of the fish he caught over the weekend. What information from the 1st Quartile does the graph give you?




A. Three fourths of the fish he caught were larger than 22 pounds.

B. The average weight of the fish he caught was 40 pounds.

C. Three fourths of the fish he caught were less than 22 pounds.

D. The largest fish he caught was 63 pounds.

Answers

Answer:

C. Three fourths of the fish he caught were less than 22 pounds.

Step-by-step explanation:

Hope it helps! At least you didn't scream Imao

Answer:

C

Step-by-step explanation:

i answered so the other person gets the brainliest they deserve!

1/3 of 3 please help I'll give 20 points​

Answers

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Please help I'll mark brainliest

A cook came across two cups and one saucer in a kitchen cupboard.

Bored for something to do, she weighed each item.

Altogether, the three items came to 12 ounces.

The larger cup with the saucer weighed exactly double of the smaller cup.

The smaller cup with the saucer weighed exactly the same as the larger cup.

What did each item weigh?

Answers

Answer: saucer 3 ounces smaller cup 3 ounces larger cup 6 ounces

Step-by-step explanation:

After eating 75% of the chocolates in a box, Dev found 6 chocolates remaining. How many chocolates were there in the box originally?

Answers

Answer:

24

Step-by-step explanation:

Let total number of the chocolates be x.

25% of x = 6 (because 100 - 75 = 25% of chocolates left).

25/100 x x = 6

x = 600/25

x = 24

Hence, 24 is the total amount of chocolates.

Hope it helps :)

Pls help as soon as possible thank you

Answers

Answer:

D

Step-by-step explanation:

F(g) falls between 0 and 49.58

evaluate the expression for h= -6.

Answers

Answer:

63-|-6| = 57

Step-by-step explanation:

63-|-6|

63-6

57

Answer:

57

Step-by-step explanation:

Substitute -6 for variable h.

[tex]63-|(-6)|\\63-6\\57[/tex]

PLEASE HELPPPPP
Write the equation of the circle in standard form from the given information. Show all work.
Center (0,0)
Diameter = 14

Answers

The answer is x^2 + y^2 = 49

Can you please help me with number 15

Answers

Answer:

142.25 miles

Step-by-step explanation:

239- 96.75

142.25

142.25 miles I think

Suppose a special discount makes the price of Nike air max shoes 10% lower. As result, there is a 20% increase in the quantity demanded for the shoes, which statement is correct ____?

Answers

It is evident from the problem statement that an overall price reduction of Nike air max shoes will lead to an increase in the demand for the shoe.

In Economics,  the relationship between price and demand is stated as follows "If all other factors remain equal, the higher the price of a good, the fewer people will demand that good. In other words, the higher the price, the lower the quantity demanded and vice versa."

In all, the Law of Demand tells us that if more people want to buy something, given a limited supply, the price of that thing will be bid higher, also of the price of something is low the demand will be high.

learn more:

https://brainly.com/question/25585026

HELPPP PLS :)
find the value of x.

Answers

Answer:

9

Step-by-step explanation:

4x - 2 = 34 measure of two legs of isosceles triangle are equal

4x = 36

x = 9

I will mark brainly, help me with this question please.​

Answers

Step-by-step explanation:

Since [tex]x[/tex] varies directly as [tex]\sqrt{y}[/tex] we can write the relation as

[tex]x = k\sqrt{y}[/tex]

where k is the constant of proportionality.

a) To solve for the k, we substitute the given values:

[tex]5 = k\sqrt{13} = k(13)[/tex]

[tex]\Rightarrow k = \dfrac{5}{13}[/tex]

b) The equation relation x and y can be written as

[tex]x = \dfrac{5}{13}\sqrt{y}[/tex]

c) When y = 9,

[tex]x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}[/tex]

David invests $10,000 in a savings account that pays 3.5% simple interest. If David

makes no withdrawals or deposits to the account, how much will be in the

account after 7 years.

Answers

Answer:

David will have $12,450 if he makes no withdrawals.

what is 9/blank= 4? i really don't know

Answers

Answer:

9/4

Step-by-step explanation:

Answer:

9/2.25 = 4

Step-by-step explanation:

9/x = 4

x = 9/4 or 2.25

-9=-12+b
What is the equation?

Answers

Answer:

The answer is 3 because you have to add 12 to both sides to isolate b.

Step-by-step explanation:

THE EQUATION IS -9=-12+b.

58. What is the equation that best represents the graph (0,5) (3, 3) (6, 1)

Answers

y = -2/3x + 5
Hope this helps!
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