Solve the Anti derivative.​

Solve The Anti Derivative.

Answers

Answer 1

Answer:

[tex]\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C[/tex]

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]:                                                                [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Trig Integration:                                                                                                           [tex]\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx[/tex]

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator:                                                         [tex]\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx[/tex][Integral] Integration Property - Multiplied Constant:                                   [tex]\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx[/tex]

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

[tex]\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx[/tex]

Step 4: Integrate Pt. 2

[Integral] Substitute u-du:                                                                               [tex]\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du[/tex][Integral] Trig Integration:                                                                               [tex]\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C[/tex][Integral] Simplify:                                                                                           [tex]\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C[/tex][integral] Multiply:                                                                                           [tex]\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C[/tex][Integral] Back-Substitute:                                                                             [tex]\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C[/tex]

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e


Related Questions

I need help ASAP what’s the answer

Answers

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer is C, from the equation y=mx+c

I need help with this

look at picture

Complementary angles

Answers

Answer:

77

Step-by-step explanation:

48 + (x-35) = 90

x-35 = 90-48

x-35 = 42

x = 42+35

x = 77

11 + 5 + 52 x 12 – 10 =
(11 + 5) + 52 x (12 - 10) =

Answers

The first one is 630 and the second one is 120

A line passes through the point (-2, 7) and has a slope of -5.

What is the value of a if the point (a, 2) is also on the line?
a. -7
b.-1
c.1
D.7

I NEED ANSWERS SOON

Answers

Answer:

[tex]\boxed{a = 3}[/tex]

Step-by-step explanation:

[tex] (using \: the \: points : (2, \: 7) = ( x_{1}, \: y_{1}\: \: ) \\ hence : (a, \: 2) = ( x_{2}, \: y_{2}\: \: ) \\ but \: m = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} = \frac{2 - 7}{a - 2} \\ - 5 = \frac{2 - 7}{a - 2} \\ - 5(a - 2) = 2 - 7 \\ - 5a + 10 = 2 - 7 \\ - 5a = - 5 - 10 \\ - 5a = - 15 \\ a = \frac{ - 15}{ - 5} \\ \boxed{a = 3}[/tex]

Find the measure of each missing angle.​

Answers

9514 1404 393

Answer:

35°145°55°125°55°

Step-by-step explanation:

The right triangles are similar, so angle 1 is congruent to the given angle, and angles 3 and 5 are complements of that.

Angles 2 and 4 are the supplements of angles 1 and 5, respectively.

  ∠1 = 35°

  ∠2 = 180° -35° = 145°

  ∠3 = ∠5 = 90° -35° = 55°

  ∠4 = 180° -55° = 125°

Which of the following is an example of an irrational number? Question 5 options: A) 3∕4 B) C) D) 74∕99

Answers

Answer:

happy to help, but c and d are not included in your question

HURRY!! 8.1=8w- 17.5. Solve for w​

Answers

W= 3.2

Need explaining?
8.1=8w-17.5 solve for W=3.2

Jonas is buying fencing to surround his garden. If his garden has a perimeter of 36 feet, and fencing costs
$10.00 a yard, how much money will he need for the fencing?

Answers

Answer:

Step-by-step explanation:

$120

X+5(_)=15 solve for x

Answers

Answer:

What's that in the parentheses.

Step-by-step explanation:

anyways, if the parentheses aren't there, its 10. X=10

If there were parentheses, the answer would be ???????????????????????????????

X-4/x-3 is less than 2x-1/2

Answers

Answer:

yes

Step-by-step explanation:

yes

Do you mean x-(4/x)-3, or (x-4)/(x-3), or x-(4/(x-3)), or ((x-4)/x)-3, or something else?

HELP ASAP PLEASE! GIVING AWAY 30 POINTS AND BRAINLIEST!

Answers

Answer:

DB!

Step-by-step explanation:

Question a: 3+3+2+2 = 10 dinners

Question b: 15-30 and 30-45, because most people choose that range.

Hope I helped!

Answer:

a) 10 b) 2-3 dollars

Step-by-step explanation:

a) 3+3+2+2

b) (2+2+3+3)/2 equal 2.5 mean, range between them is 2 to 3

Show the work for the answer

x=³√27

x = 3

Answers

Answer:

x = 3

Step-by-step explanation:

Given that,

[tex]x=\sqrt[3]{27}[/tex]

We need to show work to solve it.

We know that,

27 = 3×3×3

or

27 = (3³)

So,

[tex]x=\sqrt[3]{3\times 3\times 3}\\\\=(3^3)^{\dfrac{1}{3}}\\\\x=3[/tex]

Hence, this is the required solution.

What is the ratio of a:b, knowing that a-b/a+b = 3/5.

Answers

Answer:

4:1

Step-by-step explanation:

[tex]\frac{a-b}{a+b}[/tex] = [tex]\frac{3}{5}[/tex]

4-1 = 3

4+1 = 5

6(x - 1) = 6x - 1
what’s the answer ^^

Answers

Answer:

this is an identity which is true for all x values

Step-by-step explanation:

Perform the indicated multiplication.  We get:

6x - 1 = 6x -1

and see that this is an identity which is true for all x values.

Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now. Assuming (a) interest at an annual rate of 5% compounded annually, or (b) interest at an annual rate of 6% compounded continuously, which option should she choose under the consideration of cash value only?
A) If the interest is at the annual rate of 5%, compounded annually, then the present value of the five installments is $______. B) If the interest is at the annual rate of 6%, compounded continuously, then the present value of the five installments is $______.

Answers

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

First, we determine the value of the 5 installments using a 5% annual compounded rate.

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

A= annual payments

FV= {60,000*[(1.05^5) - 1]} / 0.05

FV= $331.537.88

PV= FV/(1+i)^n

PV= $259,768.60

At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.

Now, if the annual rate is 6% continuously compounded.

First, we need to calculate the effective interest rate:

r= e^i - 1

r= effective inerest rate

r= e^0.06 - 1

r= 0.0618

FV= {60,000*[(1.0618^5) - 1]} / 0.0618

FV= 339,443.23

PV= 339,443.23/1.0618^5

PV= $251,509.01

At an annual rate of 6% compounded continuously, she should choose the $255,000.

The Fabric storage box below is shaped like a rectangular prism how much fabric is needed to cover the exterior of the box

Answers

Answer:

2952 square centimeters are needed to cover the exterior of the box.

Step-by-step explanation:

We need to cover five external faces of the box. The surface area formula ([tex]A_{s}[/tex]), measured in square centimeters, is derived from surface area formula for parallelpiped:

[tex]A_{s} = w\cdot l + 2\cdot w\cdot h + 2\cdot l \cdot h[/tex] (1)

Where:

[tex]w[/tex] - Width, measured in centimeters.

[tex]l[/tex] - Length, measured in centimeters.

[tex]h[/tex] - Height, measured in centimeters.

If we know that [tex]w = 36\,cm[/tex], [tex]l = 23\,cm[/tex] and [tex]h = 18\,cm[/tex], then the outer surface area of the storage is:

[tex]A_{s} = (36\,cm)\cdot (23\,cm)+2\cdot (36\,cm)\cdot (18\,cm)+2\cdot (23\,cm)\cdot (18\,cm)[/tex]

[tex]A_{s} = 2952\,cm^{2}[/tex]

2952 square centimeters are needed to cover the exterior of the box.

the EXACT value of 2÷(0.01)2 is

Answers

The EXACT value of 2÷(0.01)2 is 100.

The question asks that we divide 2 by (0.01)2. Division is a basic mathematical operation. The expression in the question can be rewritten as [tex]\frac{2}{(0.01)2}[/tex].

The first step to take in order to determine the answer is to simplify the denominator. Bracket means to multiply. So, 0.01 would be multiplied by 2. 0.01 x 2 = 0.02. Now that the denominator has been simplified, divide the numerator by the denominator.

2 / 0.02 = 100

A similar question was answered here: https://brainly.com/question/22357901

The EXACT value of 2÷(0.01)2 is 100.

The question asks that we divide 2 by (0.01)2.

Division is a basic mathematical operation.

The expression in the question can be rewritten as : 2/ (0.01)2

now, we get,

The first step to take in order to determine the answer is to simplify the denominator.

Bracket means to multiply.

So, 0.01 would be multiplied by 2.

i.e. 0.01 x 2 = 0.02.

Now that the denominator has been simplified, divide the numerator by the denominator.

we get,

2 / 0.02 = 100

Learn more about the Division here:

brainly.com/question/22357901

#SPJ6

Draw the proble. give me steps. Please​

Answers

Answer:

I cant draw 4 u sry

Answer:

A. c = 3.5h + 15

Step-by-step explanation:

I can't exactly draw the problem BUT I can still help.

C represents the cost altogether but we do not know how much the total cost would be.

So we're paying $15 as a fee, no more from that.

Next, there's another fee that costs $3.50 per hour but since we wouldn't know how long we would use the kayak, hours would represent h.

Now, c = 3.5h + 15.

(In other words, the cost to rent a kayak would be $3.5 PLUS the additonal 15 one time cost.)

An angle that is one half its arc is a/n
angle.
Select one:
O a. exterior
O b. interior
O c. inscribed
O d. central

Answers

The answer is inscribed


The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.

What is the difference between 100 and 33?

Answers

Answer:

67

Step-by-step explanation:

100 - 33 = 67

The difference between 100 and 33 is 67.

The answer is 67 if you go to your calculator app and do 67+33 it equals 100

Please show work so i know how you got your answer..thank you and have a nice day<3

Answers

Answer:

V=whl=2·2.5·4=20

Step-by-step explanation:

Answer:

2880 feet³

Step-by-step explanation:

since the question is asking for cubic feet we know we're finding volume.

v=l·w·b

v=4·24·30

=2880

Simplify the expression by combining like terms 18z +9z

Answers

Answer:

z(18+9)=z*27=27z

Step-by-step explanation:

Answer:

(18+9)*z=27z

Step-by-step explanation:

) A cyclist travels a distance of 90 miles in 5 hours. What was her average speed? 2) How far along a motorway would you travel if you drove at 70 mph for 4 hours? 3) I drive to Bude in Cornwall from Sheffield in about 6 hours. The distance from Sheffield to Bude is 315 miles. What is my average speed? 4) The distance from Leeds to London is 210 miles. The train travels at an average speed of 90 mph. If I catch the 9.30 am train in London, at what time should I expect to arrive in Leeds? 5) How long will an athlete take to run 2000 m at an average speed of 4 metres per second? 6) The distance between Sheffield and Land’s End is 420 miles. a) What is the average speed of a journey from Sheffield to Land’s End that takes 8 hours 45 minutes? b) If Sam covered the distance at an average speed of 63 mph, how long would it take him?

Answers

The answer would be 649mph

729
800
9
150
8
515
125
512
612
Select all the cube numbers.

Answers

729, 9, 8, 515, 125, 512,612
(I’m not sure)

MNOP is a trapezoid with bases MN and OP. If MN = 25 and OP = 23, what is the length of the midsegment of MNOP?

Answers

Answer:

24

Step-by-step explanation:

you can get the answer from the attachment

The midsegment of a trapezoid divides the trapezoid into equal parts.

The length of the midsegment of MNOP is 24

The lengths of the base are given as:

[tex]\mathbf{MN = 25}[/tex]

[tex]\mathbf{OP = 23}[/tex]

Let the midsegment be x.

So, we have:

[tex]\mathbf{x=\frac{1}{2}(MN + OP)}[/tex]

Substitute values for MN and OP

[tex]\mathbf{x=\frac{1}{2}(25 + 23)}[/tex]

[tex]\mathbf{x=\frac{1}{2}(48)}[/tex]

[tex]\mathbf{x=24}[/tex]

Hence, the midsegment of MNOP is 24

Read more about midsegments of trapezoids at:

https://brainly.com/question/7511906

what is the answer i need help

Answers

Answer:

90/100

Step-by-step explanation:

both equal 0.9

Answer:

[tex]\frac{90}{100\\}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10}[/tex] equals [tex]\frac{90}{100\\}[/tex]

By multiplying the numerator and denominator of [tex]\frac{9}{10}[/tex] by 10, we get [tex]\frac{90}{100\\}[/tex] .

9 x 10 = 90

10 x 10 = 100

sum of two numbers is 35 and the difference is 15

Answers

Answer

IM not too sure

Step-by-step explanation:

Not too sure sorry kid

Answer:

25 and 10 are the numbers

Step-by-step explanation:

I need 2 more!! So can you help

Answers

Answer:

✔️2a + 6 + 7a

✔️2a + 7a + 6

✔️9a + 6

Step-by-step explanation:

Given:

2(a + 3) + 7a

Required:

3 equations equivalent to the given expression

Solution:

2(a + 3) + 7a = 2a + 6 + 7a = 2a + 7a + 6

= 9a + 6

From the above, we can pick 3 expressions that are equivalent to 2(a + 3) + 7a. They are:

✔️2a + 6 + 7a

✔️2a + 7a + 6

✔️9a + 6

2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD and (iv) AC.

Answers

Answer:

The answer is below.

Step-by-step explanation:

A square is a quadrilateral (has four sides and four angles) in which all the sides are equal. Also all the angle of a square are equal and measure 90°. The diagonals of a square are equal.

In square ABCD:

AB = BC = CD = AC

Given that  P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b.

a) In triangle ABP:

BC = AB (all sides of a triangle are equal)

BP = 1/2 (BC) = 1/2(AB) = 0.5AB

Using Pythagoras theorem:

AB² + BP² = AP²

substituting:

AB² + (0.5AB)² = a²

AB² + 0.25AB² = a²

1.25AB² = a²

AB² = a² / 1.25

AB² = 0.8a²

AB = √(0.8a²)

AB = a√0.8

b) In triangle ADQ:

AD = CD (all sides of a triangle are equal)

DQ = 1/2 (CD) = 1/2(AD) = 0.5AD

Using Pythagoras theorem:

AD² + DQ² = AQ²

substituting:

AD² + (0.5AD)² = b²

AD² + 0.25AD² = b²

1.25AD² = b²

AD² = b² / 1.25

AD² = 0.8b²

AD = √(0.8b²)

AD = b√0.8

c) In triangle ABD, Using Pythagoras theorem:

AB² + AD² = BD²

Substituting:

0.8a² + 0.8b² = BD²

But AB = AD (all sides of a triangle are equal). Hence AB = AD = 0.8a² = 0.8b²

BD = √(0.8a² + 0.8b²)

BD = √(1.6a²)     0.8a² = 0.8b²

BD = a√1.6

D) AC = AD (diagonal are equal)

AC = √(0.8a² + 0.8b²)

AC = √(1.6b²)     0.8a² = 0.8b²

AC = b√1.6

What is the probability of spinning a number greater than 5 on a spinner numbered 1-8 and tossing a tail on a coin

Answers

Answer:

3/16

Step-by-step explanation:

P(6,7,8 and 'T') = 3/8 x 1/2 = 3/16

Answer:

12/64

Step-by-step explanation:

We have numbers 1-8 = /8

We have the numbers 6, 7, 8 on the spinner = 3/8

We have the event it doesn't get over 8 too = 8/8-3/8 = 5/8

To use if the question has two events for spinner.

We toss a coin = H or T = 1/2

We convert a 3/8 and 1/2 to same HCF = 4/8 = ( 2x 4 = 8)

3/8 x 4/8 = 12/64

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