integral of 1÷(1+sin x) dx

Answers

Answer 1

Answer:

[tex] \tan \: x - \sec \: x + c[/tex]

Step-by-step explanation:

[tex] \int1 \div (1 + \sin \: x) \: dx \\ \\ = \int \frac{1}{1 + \sin \: x} dx \\ \\ = \int \frac{1}{(1 + \sin \: x)} \times \frac{(1 - \sin \: x)}{(1 - \sin \: x)} dx \\ \\ = \int \frac{1 - \sin \: x}{1 - \sin^{2} \: x} dx \\ \\ = \int \frac{1 - \sin \: x}{ \cos^{2} \: x} dx \\ \\ = \int \bigg( \frac{1}{ \cos^{2} \: x} - \frac{\sin \: x}{ \cos^{2} \: x} \bigg) dx \\ \\ = \int( { \sec}^{2} x - \sec \: x. \tan \: x)dx \\ \\ \purple{ \bold{ = \tan \: x - \sec \: x + c}}[/tex]


Related Questions

3 times sum of a number and nine is 12

Answers

Answer:

-5 is the missing number.

Step-by-step explanation:

Let's write the equation.

Represent the number with x.

3( x + 9 ) = 12

Now, we solve for x.

Divide by 3 on both sides.

x + 9 = 4

Now, subtract by 9 on both sides.

x = -5

The number is -5.

#teamtrees #WAP (Water And Plant)

y= 30x + 10 how do you graph this equation?​

Answers

Answer:

sdfg

Step-by-step explanation:

jh

That’s how you graph the equation

What is the slope of a line perpendicular to the line whose equation is 2x-y=5 ?

Answers

Answer:

-1/2

Step-by-step explanation:

the slope of the line 2x-y=5 is 2

a perpendicular line has the negative reciprocal of the slope of the other line

hopefully this helps :)

At a basketball game, 55% of people attending were supporting the home team, while
45% were supporting the visiting team. If the total number of people attending the
game was 520, how many people attending were supporters of the home team?

Answers

Answer:

286

Step-by-step explanation:

The football program has 14 footballs that weigh 2.57 pounds each. How much do the footballs weigh all together?

Answers

Answer:

35.98 pounds

Step-by-step explanation:

Answer:

35.98 pounds  :)

Step-by-step explanation:

2. Select ALL number families that .3251892... belongs to.

Answers

Answer:

is b

Step-by-step explanation:

got it right on the test

What grade level is a score of 235 in maps math I am really wanting to know

Answers

Answer: It should be an 8th grade level

(sorry if i'm wrong)

:(

x 0 1 2
y -4 -2 0
what is the constant rate?

Answers

Answer:

+ 2

Step-by-step explanation:

x | y

0 | -4

1 | -2

2 | 0

You are adding 2 to y every time you have a new x.

Hi can u plzz help me with these thank you!!!

1. If the diameter of a circular object is 10 feet. Find the radius and the circumference. Use 3.14 for π.


2. Find the perimeter of the window. R = 4ft

Answers

Answer:

1.

[tex]Radius = 5ft[/tex]

[tex]Circumference = 31.4\ ft[/tex]

2.

[tex]Perimeter = 25.12\ ft[/tex]

Step-by-step explanation:

Solving (1):

Given

[tex]Diameter = 10ft[/tex]

Required

Determine the radius and circumference

Radius is calculated as follows:

[tex]Radius = \frac{1}{2} * Diameter[/tex]

[tex]Radius = \frac{1}{2} * 10ft[/tex]

[tex]Radius = 5ft[/tex]

The circumference is calculated using:

[tex]Circumference = 2 * \pi * Radius[/tex]

[tex]Circumference = 2 * 3.14 * 5ft[/tex]

[tex]Circumference = 31.4\ ft[/tex]

Solving (2):

Given

[tex]R = 4ft[/tex]

Assume that the window is circular, the perimeter is calculated as follows:

[tex]Perimeter = 2 * \pi * R[/tex]

[tex]Perimeter = 2 * 3.14 * 4ft[/tex]

[tex]Perimeter = 25.12\ ft[/tex]

Which value of x makes this equation true? -9x+15+3(2-x)

Answers

Answer:

oh that easy u need to cross multiple ka girl okay?

Step-by-step explanation:

441

1) What is the sales tax of a $178 video game system if the tax rate is 5%?

Answers

Answer:

8.90

Step-by-step explanation:

178 * 5% = 8.90

Find the slope of each line using tables . try using the slope formula

Answers

Answer:

2

Step-by-step explanation:

what is 5.39 x 0.31 i need help please answer

Answers

Answer:

1.6709 is the answer for the question

Let z = 11 (cosine (StartFraction pi Over 12 EndFraction) + I sine (StartFraction pi Over 12 EndFraction) ) and w = 7 (cosine (StartFraction pi Over 12 EndFraction) + I sine (StartFraction pi Over 12 EndFraction) ).What is zw?

Answers

Answer:

B

Step-by-step explanation:

did it on edge

Answer:

B: 77 (cos (π/6) + i sin (π/6))

Step-by-step explanation:

Took the quiz.

In a classroom of 28 students, 75% of the students have met their reading goal. How many students have NOT met their reading goal?

Answers

Answer:

you divide 28 with 4

Step-by-step explanation:

Order of Operations with and without variables

Answers

Answer:

51

Step-by-step explanation:

First, we plug 3 into the x values to get:

45-3+9

Then we do order of operations to get 51 as our answer.

2x² - 3x² + 3x + 4x - 7 - 7​

Answers

Answer : x^2 + 7x - 14

Explanation : I simplified it

there are 2 donkeys for every 5 horses on a farm. how many donkeys and horses could be on the farm?

4 donkeys and 7 horses..
8 donkeys and 20 horses..
12 donkeys and 15 horses..
17 donkeys and 20 horses..

Answers

Answer:

B.  8 donkeys and 20 horses..

Step-by-step explanation:

Because

2*4=8

5*4=20

Answer:

8 donkeys and 20 horses

Step-by-step explanation:

2/5 * 4 over 4 = 8/20


Can someone help me find x
And why?
PLZZZ I WILL GIVE U 20 POINTS

Answers

Answer: x is on the side we’re the prime example if found if u have a example

Step-by-step explanation:

there are 4 white marbles 6 red marbles and 2 blue marbles and 4 green marbles if the marble is chosen randomly what is the probability it is not green

Answers

3/4 or 75%

There are 4 green marbles out of 16 marbles so the chance of not picking green is 12/16 so simplify to 3/4 and convert to percentage

find the exact length of the third side

Answers

Step-by-step explanation:

if the length of the third side = a

a² + 13² = 85²

a² + 169 = 7,225

a² = 7,225 - 169

a² = 7,056

a = square root 7,056

a = 84

So, the length of the third side is equal 84 unit.

Answer:

84

Step-by-step explanation:

According to Pythagoras theorem

x²+y²=z²

x=√z²-y²

x=√85²-13²

x=√7225-169

x=√7056

x=84

in right triangle RST altitude TV is drawn to hypotenuse RS If RV = 12 and RT = 18, what is the length of SV

Answers

Answer:

12

Step-by-step explanation:

Given that:

RV = 12 and RT = 18

Kindly refer to attachment for triangle diagram:

Using the altitude on hypotenus theorem :

Length of RS = 12 + a

RT² = RV * RS

18² = 12 * (12 + a)

324 = 12(12 + a)

324 = 144 + 12a

324 - 144 = 12a

180 = 12a

Divide both sides by 12

180/12 = a

15 = a

Hence, SV = 12

0.5(x+2,000)=3,000

solve for x

Answers

.5x + 1000= 3000
.5x=2000
X= 4000
First step subtract 1000
Second step divide by 0.5
0.5x3000=6000

X+2000=6000

X=6000-2000

X=4000

What’s the answer to
3/5 + 9/20

Answers

Answer:

= 21/20

Step-by-step explanation:

You must change 3/5 to 12/20 so that the denominators match,

12/20 + 9/20

add the numerators

12 + 9 = 21

21/20

Write the following number beds from one to number of the place value chart 5×100+8×1+2×1/10+3×1/100+1×1/1000 equals what number in standard form

Answers

Answer:

Hundreds: 5

Tens: 0

Ones: 8

Tenths: 2

Hundredths: 3

Thousandths: 1

Standard form: 508.231 or 5.08231 x 10^2

What is the length of AB? Help ASAP

Answers

Answer:

6/8

Step-by-step explanation:

simplify and find the slope

6/8 is the answer you’re looking for

STEAM: The boiling pint of water is affected by changes in elevation. Use the expression of -2A/1000 where a represents the altitude in feet to find the number of degrees Farenhite at which the boiling point of water changes at altitude 5,000 feet

A) -10°F B) 20°F C) 10°F D) -20°F

Answers

Answer:

A) -10°F

Step-by-step explanation:

Given that:

Boiling point of water gets affected when there is a change in the elevation.

Expression to represent the temperature i.e. boiling point w.r.to altitude [tex]A[/tex] is given by the equation:

Temperature in [tex]^\circ F[/tex] = [tex]\frac{-2A}{1000}[/tex]

Given that, the altitude, [tex]A[/tex] = 5,000 feet

To find:

The number of degrees Farenhite at which the boiling point of water will change.

Solution:

Here, we are given the expression:

Temperature in [tex]^\circ F[/tex] = [tex]\frac{-2A}{1000}[/tex]

And value of altitude, [tex]A[/tex] = 5,000 feet

Let us put the value of [tex]A[/tex] in the equation and let us find the value of temperature in [tex]^\circ F[/tex].

Temperature in [tex]^\circ F[/tex] =

[tex]\frac{-2\times 5000}{1000}\\\Rightarrow -2\times 5\\\Rightarrow \bold{-10^\circ F}[/tex]

Therefore, the answer is:

A) -10°F

Favorite song smh I have to type 20 characters

Answers

I got a telling and ensure Lsns r do I kendn send it

Answer:

My 2 fav songs are im a mess and your gonna go far kid :D

Step-by-step explanation:

Have a good day! And god bless! <3

I need help with this ASAP

Answers

Answer:

X=31

Step-by-step explanation:

X-7+1+5x=180

6x-6=180

6x=180+6

6x=186

x=186÷6

X=31

For many waiting line situations, the arrivals occur randomly and independently of other arrivals and it has been found that a good description of the arrival pattern is provided by a

Answers

Answer:

Poisson Probability distribution.

Step-by-step explanation:

We are told that arrivals occur randomly and independently of other arrivals. This can be analyzed with Poisson Probability distribution because In statistics Poisson distribution is simply a statistical distribution that shows the number of times an event will likely occur within a specified amount of time.

This distribution is normally used for independent events which occur at a constant rate within a given time interval.

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