Find the indefinite integrals, if possible, using the formulas and techniques you have studied so far in the text.(a) 11 x4 dxThis integral can be evaluated using the basic integration rules.This integral cannot be evaluated using the basic integration rules. (b) 8x1 x4 dxThis integral can be evaluated using the basic integration rules.This integral cannot be evaluated using the basic integration rules. (c) 3x31 x4 dxThis integral can be evaluated using the basic integration rules.This integral cannot be evaluated using the basic integration rule

Answers

Answer 1

Answer:

a) This integral can be evaluated using the basic integration rules. [tex]\int 11x^{4}dx = \frac{11}{5} x^{5}+C[/tex]

b) This integral can be evaluated using the basic integration rules. [tex]\int 8x^{1}x^{4}dx=\frac{4}{3}x^{6}+C[/tex]

c) This integral can be evaluated using the basic integration rules. [tex]\int 3x^{31}x^{4}dx=\frac{x^{36}}{12}+C[/tex]

Step-by-step explanation:

a) [tex]\int 11x^{4}dx[/tex]

In order to solve this problem, we can directly make use of the power rule of integration, which looks like this:

[tex]\int kx^{n}=k\frac{x^{n+1}}{n+1}+C[/tex]

so in this case we would get:

[tex]\int 11x^{4}dx=11 \frac{x^{4+1}}{4+1}+C[/tex]

[tex]\int 11x^{4}dx=11 \frac{x^{5}}{5}+C[/tex]

b) [tex]\int 8x^{1}x^{4}dx[/tex]

In order to solve this problem we just need to use some algebra to simplify it. By using power rules, we get that:

[tex]\int 8x^{1}x^{4}dx=\int 8x^{1+4}dx=\int 8x^{5}dx[/tex]

So we can now use the power rule of integration:

[tex]\int 8x^{5}dx=\frac{8}{5+1}x^{5+1}+C[/tex]

[tex]\int 8x^{5}dx=\frac{8}{6}x^{6}+C[/tex]

[tex]\int 8x^{5}dx=\frac{4}{3}x^{6}+C[/tex]

c) The same applies to this problem:

[tex]\int 3x^{31}x^{4}dx=\int 3x^{31+4}dx=\int 3x^{35}dx[/tex]

and now we can use the power rule of integration:

[tex]\int 3x^{35}dx=\frac{3x^{35+1}}{35+1}+C[/tex]

[tex]\int 3x^{35}dx=\frac{3x^{36}}{36}+C[/tex]

[tex]\int 3x^{35}dx=\frac{x^{36}}{12}+C[/tex]


Related Questions

Help plz....................

Answers

Answer with  explanation:

y+1 = 26     ;      y = 26-1 = 25

x-2 = 19           ;    x = 19+ 2 = 21

I hope im roght!!

PLEASE ANSWER FAST!!!!!

Answers

Answer:

Step-by-step explanation:

if the function is x the answer is 1 hope it helps

Please help me lol ......................

Answers

Answer:

A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

simple logic

What are the answers to the puzzle?

Answers

Answer:

1) 25°

2) 155°

3) 25°

4) 25°

5) 110°

6) 30.5°

7) 41°

Step-by-step explanation:

5) 5x + 15 = 8x - 42,  3x = 57,   x= 19, ∠CDE = 5(19) + 15 = 110°

6) 3x + x + 4 + 70° = 180°,  4x = 106°, x = 26.5°, ∠ABC = 26.5° + 4° = 30.5°

7) 2x + x + 4 + 65° = 180°, 3x = 111°, x = 37°, ∠MNO = 37° + 4° = 41°

Is 4(4f-8)+5= 16f+37

Answers

4(4f-8)+5= 16f-27
that’s the right answer

9.85xs;s=4
help me. please

Answers

Answer:

39.4

Step-by-step explanation:

9.85 * (4) = 39.4

Help I’ll give brainliest

Answers

Answer:

8

888888888888888888888888888

The first person that guess what game I play get free games...



Answers

rblx or among us
and I need help in math good luck​

Answers

Answer:

amoug us

Step-by-step explanation:

) Express each of these statements using mathematical and logical operators, predicates, and quantifiers, where the domain consists of all integers. a) The sum of two negative integers is negative. b) The difference of two positive integers is not necessarily positive. c) The sum of the squares of two integers is greater than or equal to the square of their sum. d) The absolute value of the product of two integers is the product of their absolute values.

Answers

Answer:

a. ∀ a, b ∈ Z, if a < 0 ∧ b < 0 ⇒ a + b < 0

b. ∀ a, b ∈ Z, if a > 0 ∧ b > 0 ⇒ a - b < 0 ∨ a - b > 0

c. ∀ a, b ∈ Z, a² + b² ≥ (a + b)

d. ∀ a, b ∈ Z, |ab| = |a||b|

Step-by-step explanation:

a. The sum of two negative integers is negative.

First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, if a and b are negative, we write if a < 0 ∧ b < 0 where the logical operator ∧ represents "and". So, we have the statements ∀ a, b ∈ Z, if a < 0 ∧ b < 0. Then finally, we use the logical operator ⇒ to imply the summation of the two integers as ⇒ a + b. And since we are to show that their sum is less than zero, we write ⇒ a + b < 0.

Combining this statement with the previous expressions, we have

∀ a, b ∈ Z, if a < 0 ∧ b < 0 ⇒ a + b < 0

b. The difference of two positive integers is not necessarily positive.

First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, if there exists a and b that are positive, we write if a > 0 ∧ b > 0 where the logical operator ∧ represents "and". So, we have the statements ∀ a, b ∈ Z, a > 0 ∧ b > 0. Then finally, we use the logical operator ⇒ to imply the difference of the two integers as ⇒ a - b. And since we are to show that their difference is either less than zero or greater than zero, we write ⇒ a - b < 0 ∨ a - b > 0 where ∨ implies the logical operator "or".

Combining this statement with the previous expressions, we have

∀ a, b ∈ Z, if a > 0 ∧ b > 0 ⇒ a - b < 0 ∨ a - b > 0

c. The sum of the squares of two integers is greater than or equal to the square of their sum.

First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, since we are dealing with the sum of the squares of each integer, we write a² + b². And, we are to show that this sum is greater than the sum of the individual integers, we write their sum as a + b, and we show the previous sum to be greater than or equal to this as a² + b² ≥ (a + b).

Combining this statement with the previous expressions, we have

∀ a, b ∈ Z, a² + b² ≥ (a + b)

d. The absolute value of the product of two integers is the product of their absolute values.

First, we take the quantifier ∀ and write the two integers a and b as a element of the set of integers Z as ∀ a, b ∈ Z. Now, since we are to show that absolute value of the product of the integers equals the product of the absolute value of the individual integers, we write the that absolute value of the product of the integers as |ab| and the product of the absolute value of the individual integers as |a||b|.

Since we are to show that this expression and the previous expression are equal, we write |ab| = |a||b|.

Combining this statement with the previous expressions, we have

∀ a, b ∈ Z, |ab| = |a||b|

If you owned a house, and the assessed value was $435,000.00, how much in property taxes would you have to pay per year if the rate was 0.79%? (be sure to use $ and a decimal. No need to use a comma)

a bit of help

Answers

The Amount of property taxes you would have to pay per year if the rate was 0.79% is $3,436.50.

If you owned a house and the assessed value was $435,000.00, the amount of property taxes you would have to pay per year

if the rate was 0.79% can be calculated as follows:SolutionTo calculate the amount of property taxes, multiply the assessed value by the tax rate.

We can represent this mathematically as:P = R × Vwhere:P = Property taxesR = Tax rateV = Assessed Value

We are given that:R = 0.79%V = $435,000.00

We need to convert the tax rate to a decimal value before we can use it in our calculation. This can be done by dividing the percentage value by 100. Therefore:R = 0.79 ÷ 100= 0.0079

Using the formula above, we can now calculate the property taxes as:P = R × V= 0.0079 × $435,000.00= $3,436.50

Therefore, the amount of property taxes you would have to pay per year if the rate was 0.79% is $3,436.50.

For more questions on Amount.

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How will the graph of the function f(x)=3^x translate the function is changed to f(x)=3(x-2)

Answers

Answer:shift two units to the right

Step-by-step explanation:

And can someone answer this question as well please

Answers

Answer:

a) 3

b) 725

c) 12100

d)3900

A dilation produces a smaller figure. Which is a possible scale factor?
0 -2
O 1/3
O 1
O4

Answers

Answer:

1/3

Step-by-step explanation:

1.5x= 3 help me I don't know what this means

Answers

Answer:

x = 2

Step-by-step explanation:

simple

just divide 3 by 1.5 to get x

3 / 1.5 = 2

so

x = 2

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

hehe lol? math math math​

Answers

Answer:

lol

Step-by-step explanation:

Answer:

math kinda sucks. :) Brainliest pls???

Step-by-step explanation:

question plz helpppppppppp

Answers

Answer:

the answer is 38.25

Step-by-step explanation:

45-15%

=38.35

Answer:

$6.75

Step-by-step explanation:

To solve any percent problem, u can use the equation part         %

                                                                                           -------   =   ---

                                                                                         whole       100

(the lines are fraction bars btw, when u right out the problem, write it as fractions)

In this problem, the whole is 45, because that is the original, or whole price. The % is 15, because u want to find 15%. The part would be x, because that's what u want to find. Cross multiply, so ur problem should look like this:

100x = 675.

Then, divide 675 by 100 to get x = 6.75.

So Natalie saves $6.75.

hope this helps!

Find the value of -7 + 3(-12) ÷ (-3).

Answers

answer:

5 is the answer

Step-by-step explanation:

I don't know how I got my answer but please try

PLEASE HELP ITS DONE IN 8 HOURSS!!!!!!

Answers

-5.25 is shown inside the points
all the other answers are outside of the points, hope this helps !

Please help!!! I'm very confused! Im giving points for it but if please tell the truth <3

Answers

Answer:

A

Step-by-step explanation:

It actually trying to trick you with a double negative

Answer:

A

Step-by-step explanation:

Squares do have right angles, if they did not have to then all other ssquares with no right angles would be considered rhombuses.

The question is sking which does not apply, a does not apply but thats what theyre asking so its a

6=2(y+2)
I. Don’t get it

Answers

Answer:

1

Step-by-step explanation:

6=2*y+4

6-4=2*y

2=2*y

y=2/2

y=1

655,325 to the nearest hundred thousands

Answers

Answer:

700,000

Step-by-step explanation:

55,325 is closer to 100,000 than it is to 0, so the hundred-thousands place would round up.

Answer:

655,325

Step-by-step explanation:

Im pretty sure it would just stay the same because 3 is not enough to bring the 5 up to 6.

what is the answer to this question 108= ​

Answers

Umm what’s the question??

Find the coordinates of the center and the measure of the radius for a circle whose equation is (x - 3)^2 + (y - 7)^2 = 2.
A. center = (3,7), radius = √2
B. center = (3,7), radius = 1
C. center = (-3, -7), radius =4
D. center = (-3, -7), radius =1

Answers

Answer:

A

Step-by-step explanation:

Equation for a circle of radius r, centered at (h,k):

(x-h)² + (y-k)² = r²

The coordinates of the center and the measure of the radius for a circle given are center = (3,7), radius = √2.

What is a circle?

A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the center. A circle is also the set of all points that are equidistant from the center.

Given is an equation of a circle, we need to find coordinates of the center and the measure of the radius for a circle,

The equation of the circle =

(x - 3)² + (y - 7)² = 2

The standard equation for a circle of radius r, centered at (h,k):

(x-h)² + (y-k)² = r²

Comparing both we get,

(h, k) = (3, 7)

r² = 2

r = √2

Hence, the coordinates of the center and the measure of the radius for a circle given are center = (3,7), radius = √2.

Learn more about circle, click;

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sabrina is making a snack mix. She uses these items. peanuts 5/6, chocolate chips 1/3, granola 1/2, raisins 3/4. What is the total weight Sabrina used

Answers

Answer:

29/12

Step-by-step explanation:

5/6+1/3+1/2+3/4

10/12+4/12+6/12+9/12

14/12+6/12+9/12

20/12+9/12

29/12

Employees at Pete's Packaging earn time-and-a-half pay for all hours worked beyond 40 hours.
Last week an employee worked a total of 44.5 hours. How much overtime pay did the employee
earn if his regular pay rate is $12.28 per hour?

Answers

Answer:

82.89

Step-by-step explanation:

You have to start I figuring out how much overtime pay is per hour. Time and a half pay on $12.28 is $18.42. Working a total of 44.5 hours means that 4.5 hours for overtime. $18.42 x 4.5= $82.89 overtime pay.

Treven puts 8 gallons of gas in his car air pays $22.00 what is the cost of 1 gallon of gas complete the table

Answers

Answer:

the cost of each gallons is 8÷22.00=$36

Look for Patterns Sally sees
a pattern in these numbers. Describe
the pattern.
500, 501, 502, 503, 504, 505

Answers

Answer:

Step-by-step explanation:

It is an arithmetic sequence. The nth term = 499 + n

find the common difference of the arithmetic sequence 10, 1, -8...​

Answers

The answer to your question is -9

Please help!!
I need to factor P(x)=x^4+50x^2+625
I thought the answer was P(x)=(x^2+25)^2
But it isn’t could someone please help with the answer?

Answers

x

4

+

50

x

2

+

625Rewrite  

625

as  

25

2

.

u

2

+

50

u

+

25

2

Check the middle term by multiplying  

2

a

b

and compare this result with the middle term in the original expression.

2

a

b

=

2

u

25

Simplify.

2

a

b

=

50

u

Factor using the perfect square trinomial rule  

a

2

+

2

a

b

+

b

2

=

(

a

+

b

)

2

, where  

a

=

u

and  

b

=

25

.

(

u

+

25

)

2

Replace all occurrences of  

u

with  

x

2

.

(

x

2

+

25

)

2

What is the probability of landing on red and rolling a number greater than 2?

Answers

Answer: 1/4 I think

Step-by-step explanation:

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