1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ainat [17]
2 years ago
12

Integral of (sin(2x) + cos(2x)) dx=

Mathematics
1 answer:
Vinil7 [7]2 years ago
3 0

\displaystyle \int (\sin 2x + \cos 2x)~ dx\\\\=\displaystyle \int \sin 2x ~dx + \displaystyle \int \cos 2x ~ dx\\\\=-\dfrac{\cos 2x}2 + \dfrac{\sin 2x}2 +C\\\\=\dfrac{\sin 2x - \cos 2x}2+C

You might be interested in
PLEASE HELP ILL MARK BRAINLIEST !!!
Alexus [3.1K]

Answer:

a) the common difference is 20

b) x_8=115 , x_{12}=195

c) the common difference is -13

d) a_{12}=52, a_{15}=13

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: x_n=x_1+(n-1)d

We know common difference d= 20, we need to find x_1

Using x_3=16 we can find x_1

x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25

So, We have x_1 = -25

Now finding x_8

x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115

So, \mathbf{x_8=115}

Now finding x_{12}

x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195

So, \mathbf{x_{12}=195}

c) what is the common difference of the sequence a_m

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: a_n=a_1+(n-1)d

We know common difference d= -13, we need to find a_1

Using a_7=104 we can find x_1

a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195

So, We have a_1 = 195

Now finding a_{12} , put n=12

a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52

So, \mathbf{a_{12}=52}

Now finding a_{15} , put n=15

a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13

So, \mathbf{a_{15}=13}

5 0
3 years ago
What is the solution to the system of equations <br><br> 3x+2y=39<br> 5x-y=13
Marta_Voda [28]

3x + 2y = 39

5x - y = 13

Multiplying the last by two:

10x - 2y = 26

Adding to the first

13x = 65

x = 5

y = 5x-13 =25-13=12


Check:

3(5)+2(12)=39 good

5(5)-12=13 good


Answer: x=5, y=12


8 0
3 years ago
What is the simplest form of the monomial given in factored form
IRINA_888 [86]
8d³e²f. ..................................
7 0
2 years ago
What is the value of y
mixas84 [53]
840? Im not sure im sorry
8 0
3 years ago
Read 2 more answers
What is the decimal form for nine and fifteen thousandths?
nikdorinn [45]
The decimal form for nine and fifteen thousandths is 09.15
3 0
2 years ago
Other questions:
  • 3x + 2y= 9. How do I solve this problem?
    9·1 answer
  • Suri solved the equation x^2=49 and found that x = 7. What error did Suri make? 15 points to answer​
    14·1 answer
  • If you put a down payment on a house of less than 20% of its value you typically have to pay
    14·2 answers
  • Explain how you would graph the following set of parametric equations by plotting points and describing the orientation.
    14·2 answers
  • The following steps are used to write the polynominal expression 3(x+4y)+5(2x-y)
    6·1 answer
  • Algebra question I need the work showed with it.
    5·2 answers
  • Find only perimeter of shape length 574.0 cm and width 487.7cm
    9·1 answer
  • Will the graph of y = (7.25x)^2 be stretched or compressed horizontally or vertically when compared to the parent function y = x
    5·1 answer
  • Use the first derivative of the following <br><img src="https://tex.z-dn.net/?f=f%28x%29%20%5Cfrac%7B1%7D%7Bx%20-%201%7D%20" id=
    9·1 answer
  • There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players o
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!