Evaluate the following integral using complex exponentials and write the result in complex exponential form. do not include the arbitrary constant.
∫ e^7x cos (x) dx

Answers

Answer 1

Therefore, the arbitrary constant is not required, our final answer is (1/2)[(1/(7+i))e^(7x + ix) + (1/(7-i))e^(7x - ix)]

To evaluate this integral using complex exponentials, we can use Euler's formula: e^(ix) = cos(x) + i sin(x). We can rewrite cos(x) as the real part of e^(ix), and then use the property that ∫ e^(ax) dx = (1/a) e^(ax) to solve the integral.
First, we rewrite the integral as ∫ (1/2) e^(7x + ix) + (1/2) e^(7x - ix) dx.
Then, using the above property, we get the answer in complex exponential form:
(1/14) e^(7x + ix) + (1/14) e^(7x - ix) + C, where C is the arbitrary constant.
To evaluate the integral ∫e^(7x)cos(x) dx using complex exponentials, we need to recall Euler's formula:
cos(x) = (e^(ix) + e^(-ix))/2
Now, substitute cos(x) with Euler's formula in the integral:
∫e^(7x)((e^(ix) + e^(-ix))/2) dx
Multiply e^(7x) into the parentheses:
(1/2)∫(e^(7x + ix) + e^(7x - ix)) dx
Now, integrate with respect to x:
(1/2)[(1/(7+i))e^(7x + ix) + (1/(7-i))e^(7x - ix)] + C

Therefore, the arbitrary constant is not required, our final answer is (1/2)[(1/(7+i))e^(7x + ix) + (1/(7-i))e^(7x - ix)]

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Related Questions

help asap pleaseeee (if u do ily)))

Answers

Answer:

B) 120

Step-by-step explanation:

180 - 60 = 120

Hope that helps!

Answer:

B. 120

Step-by-step explanation:

its bigger than 90 so i did process of elimination

solve for b
ցb – m = 9

Answers

Answer:

I couldn't write it since I don't have the format, but it is attached.

Un reloj marca las 4:55 horas . Que valor tiene el ángulo que forman las manecillas? Escribe tu resultado considerando el ángulo positivo y el ángulo negativo.​

Answers

Answer: what does this say please help

Step-by-step explanation:


1. In the expression x2, 2 is what we call
A. Base
B. Exponent
C. Multiple ​

Answers

Answer:

hello! if you're talking about x², then 2 is what we call: B. Exponent.

2 would be the exponent. X would be the base.

Si un terreno tiene 15 m de ancho y 40 m de largo y ademas al lado existen 5 terrenos identicos ¿cual es el area de todos los terrenos?​

Answers

no se boy a septimodkxkdkdkdkdkdoi

I need help with my home work pls

Answers

Ooh feel bath for you, sorry I can’t help I’m in 5th grade

If a model of a dinosaur is 3.75 feet and the scale factor for the actual dinosaur is 1:24. What is the size, in feet, of the actual dinosaur?

Answers

Answer:     120

Step-by-step explanation:

Next, write ratios to represent the unknown actual length and width of the display to the scale length and width of the display.

LengthWidth=scaleactual=4l=scaleactual=8w

Then, write two proportions by setting the two length ratios equal to one another and the two width ratios equal to one another. The given unit is feet.

LengthWidth=4l=1160=8w=1160

Next, cross multiply each equation.

LLWW=4×160=640 feet=8×160=120 feet

Then, to find the area of the display, multiply length times width.

The actual size of the dinosaur is 90 feet.

What is a scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

A model of a dinosaur is 3.75 feet,

and the scale-factor for the actual dinosaur is 1:24.

So,

the size of the actual dinosaur = model size x the scale-factor

The size of the actual dinosaur = 24 x 3.75

The size of the actual dinosaur = 90 feet.

Therefore, the actual size is 90 feet.

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what is the y value when x=-1?

what is the y value when x=0?

what is the y value when x=-1?

Answers

Answer:

2

0

-2

Step-by-step explanation:

sub x into formula

-2(-1)=2

-2(0)=0

-2(1)=-2

Answer:

60

Step-by-step explanation:

A line graph titled Car Mileage for a Hybrid Car has number of gallons on the x-axis, and number of miles on the y-axis. 1 Gallon is 60 miles, 2 gallons is 120 miles, 3 gallons is 180 miles, and 4 gallons is 240 miles.

What is the value of y when the value of x is 1?

A parking lot has the shape of a parallelogram. The length of two adjacent sides are 70 meters and 100 meters. The angle between them is 70°. What is the area of the parking lot?

Answers

the answer is 6577.85 m^2

The area of the parking lot is 4606 square meter.

What is parallelogram?

It is a special type of quadrilateral that has both the pairs of opposite sides parallel and equal.

What is the area of parallelogram?

The area of a parallelogram is the product of its base and height.

We have,

length of two adjacent sides are 70meters and 100meters.

And base of parallelogram is 70m.      (length of parallelogram is its base)

Angle between the adjacent sides is 70 degrees.

Let, side AB and BC be the two adjacent sides whose lengths are 70m and 100m.And h be the height of the parallelogram.

For the height of the parallelogram

In ΔADE, we have

[tex]sin70=\frac{DE}{AD}[/tex]           [tex](sinx=\frac{perpendicular}{hypotenuse})[/tex]

⇒ [tex]0.9397=\frac{h}{70}[/tex]

⇒ [tex]0.9397[/tex]×70[tex]=h[/tex]

⇒ h=65.8m

Formula to find the area of parallelogram:

Area= base× height

so, the area of parking lot=base × height

substitute the value of base and height of the parallelogram in the above formula.

Therefore,

[tex]Area=65.8[/tex]×[tex]70[/tex]

[tex]Area=4606m^{2}[/tex]

Hence, the area of the parking lot is 4606 square meter.

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In Fluorescent higher secondary school there are 53 students in class 8. If number of boys is 3 morethan that of number of girls find.
a. Equation representing the number os students.
b. The number of Boys and Girls.​

Answers

Answer:

a. 3g + g = 53

b. 40 boys and 13 girls

Step-by-step Explanation:

(3g = number of boys)

(g = number of girls)

3g + g =53

4g = 53

g = 13.2

53 - 13.2 = 39.8 (boys)

we round to the nearest tenth on both

girls 13.2---13

boys 39.8---40

what is the standard form of (-2/3)x - 4

( slope intercept )

Answers

Answer:

m=0,b for -2/3 x-4

Step-by-step explanation:

..........

Please Help!! I will give Brainliest to the correct answer!!

Evaluate 12.3s +11.9t when s= 3 and t = 4



Thank you so much

Answers

Answer:

84.5

Step-by-step explanation:

12.3(3)+11.9(4)=84.5

Answer:

87.5

Step-by-step explanation:

12.3 x 3= 39.9=s

11.9 x 4= 47.6=t

47.6 + 39.9= 87.5

Heidi is driving 200 miles. She has finished 80% of the drive. How many miles is 80% of Heidi's drive.

Answers

Answer:

160 miles

Step-by-step explanation:

200 * 0.8 is 160

Answer:

160 miles

Step-by-step explanation:

80/100*200

80*2

160

YOU CAN MARK ME AS BRAINIEST IF YOU WANT

please help me with this

Answers

Answer: A. 2[tex]\sqrt[3]{6}[/tex]

Step-by-step explanation:

Please help me to solve the 7th part !​

Answers

Answer:

i don't know

Step-by-step explanation:

sorry sorry sorry berry much

Which inequality has a closed circle when it is graphed on a number line?
x greater-than 0.4
x greater-than negative 3
x less-than 4
x greater-than-or-equal-to 3

Answers

Answer:

Less than 4 I guess??

This part I have scribbled so I can answer

no x Ehud ihehiexbhhenxkjwbhxnwbxhuebxbuebxh

Answer:

D

Step-by-step explanation:

Help me out

Length = m

Answers

[tex]perimeter = a + b + c[/tex]

[tex]perimeter = 4 + 3 + c[/tex]

//

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {4}^{2} + {3}^{2} = {25}^{2} [/tex]

[tex] \sqrt{25} = 5[/tex]

[tex]c = 5 \: meters[/tex]

//

[tex]perimeter = 4 + 3 + 5[/tex]

[tex]perimeter = 12 \: meters[/tex]

//

[tex]the \: length \: of \: the \: fencing \: is\: 12 \: meters[/tex]

Help please
3 |X-4| +1 = 19

Answers

The answer would be X = 10

Can you guys help me!!!

Answers

Answer:

I guess its the 3rd one not sure

what is bigger 6/5 or 4/5?

Answers

Answer:

6/5 is bigger

Step-by-step explanation:

6/5 simplifies to 1 and 1/5 which is greater than just 4/5

Answer:

6/5, the numerator is the number that determins the amount that is an improper fraction actually, the proper way of writing it is 1 and 1/5 but both are acceptable. most teachers prefer it this was though.

Step-by-step explanation:

hope this helps

This graph shows how the total distance Jack has walked depends on the number of trips he has made to school.

ASAP BEFORE 11:59

Answers

2 kilometers per trip

Answer:

whats the question

Step-by-step explanation:

thats the answer

Can someone plz help me with this?

Answers

Answer:

D

Step-by-step explanation:

because the odds have to be even if the possobility number is even

In triangle KLM, the measure of angle M is 90 degrees, the measure of angle K is 75 degrees, and LM is equal to 6.3 feet. Find the length of KL to the nearest tenth of a foot.

Answers

Answer:

6.5feet

Step-by-step explanation:

Using the SOH CAH TOA identity

<K = 75 degrees

opposite = LM = 6.3 feet

Hypotenuse = KL

sin theta = opp/hyp

sin 75 = 6.3/x

x = 6.3/sin75

x = 6.3/0.9659

x = 6.5feet

Hence the length of KL to the nearest tenth of a foot is 6.5feet

HELP AND WILL GIVE BRAINLIEST!!! Solve for x

Answers

Triangles add to 180.

180 - 57 - 43 = 80.

Vertical angles are always equal, so they are both 80 degrees in this case.

Now we know the top triangle has 80 + 2x = 180

2x = 100

Therefore x is 50 degrees.

Answer:

let the opposite angle of 43=y

57°+43°+y=180°[by sum of all angle is 180°]

100+y=180°

y=180°-100

y=80°

opposite angle of x is equal to the 80°

so the equation will be like this

x+x+80°=180°

2x+80°=180°

2x=180°-80°

2x=100

x=100/2

x=50°

so the value of x is 50°

4. (Claim 1 Example)
Bob uses a 20 foot ladder to paint a section of his house that is 16 feet high.
H
16 ft
Ladder
20 ft

Х
Ground
Select all equations that can be used to solve for e.
12
12
sino =
cos 0 =
A.
20
B.
20
tan
C.
12
20
16
sin =
20
16
cos O =
20
tan
16
20
D.
E.
F.

Answers

Answer:

D

Step-by-step explanation:

using Sohcahtoa we know that we can only use Soh (since we have the opposite,16 and the hypotenuse, 20)

D is the only one that uses the correct equation of S = o/h

(this explanation isn't the best so please search up Sohcahtoa if it doesn't make sense)

its d hope this helps

There are 4 red balls in a bag and an unknown number of white balls. If we randomly
choose a ball from the bag, the probability of getting a white ball is larger than the
probability of getting a red ball. What might be the number of white balls in the bag?

Answers

Step-by-step explanation:

well if there were 5 white the probability is 5/9 vs 4/9 for red. so the number of white balls is anything greater than or equal to 5

plzz write with formula and explanation plzzzzzzzz

Answers

Given:

[tex]-\dfrac{33}{16}[/tex] should be divided by a number to get [tex]-\dfrac{11}{4}[/tex].

To find:

The unknown number.

Solution:

Let [tex]-\dfrac{33}{16}[/tex] should be divided by x to get [tex]-\dfrac{11}{4}[/tex].

[tex]\dfrac{-\dfrac{33}{16}}{x}=-\dfrac{11}{4}[/tex]

[tex]-\dfrac{33}{16}=-\dfrac{11}{4}x[/tex]

Multiply both sides by 16.

[tex]-33=-44x[/tex]

Divide both sides by -44.

[tex]\dfrac{-33}{-44}=x[/tex]

[tex]\dfrac{3}{4}=x[/tex]

Therefore, the unknown number is [tex]\dfrac{3}{4}[/tex].

10/27=a/135
what is the answer for this equation?

Answers

Answer:

So we have this equation:

10/27 =  a/135

What we can do is multiply  both sides by 27 and 135:

10*135 = a * 27

1350 = 27a

a = 1350/27. = 50.

H
(3n - 15)°
(2n + 5)º
E
F
G
What is the value of n ?

Answers

I’m not good at math but I’ll help you the value of n is 20


List the first five prime numbers ​

Answers

Answer:

2,3,5,7,11

Step-by-step explanation:

see above for the first five prime numbers

Answer:

2, 3, 5, 7, 11

hope this helps

have  a good day :)

Step-by-step explanation:

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