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Kazeer [188]
2 years ago
15

Evaluate the integral (e^x)/((e^2x)+3) from 0 to infinity

Mathematics
1 answer:
elena55 [62]2 years ago
3 0
So, from our equation
u = e^x
du/dx = e^x du = e^xdxthe integral would be: 

du/(u^2 + 3)

Using the boundaries 1 to infinity
As, e^0 = 1.the solution for this integral will be

(1/(3^0.5)) * arctan(u/(3^0.5))Plugging the boundaries

(1/(3^0.5)) * (90 - 30) = 60/(3^0.5)
=0.6046
You might be interested in
How do you do <br><br>f(x)=12x+3 2units left<br>g(x)=<br><br><br>please help I'm confused ​
Mkey [24]

Answer:

g(x) = 12x + 27

Step-by-step explanation:

Take a point in the f(x).

f(0) = 12(0) + 3

f(0) = 3

A point on f(x) is (0,3).

Move the point 2 units left. It will make the x-coordinate decrease by 2.

0 - 2 = -2

A point on g(x) is (-2,3).

Substitute the point and the same slope into the equation of a line. The slope did not change.

y = mx + b

3 = 12(-2) + b

3 = -24 + b

b = 3 + 24

b = 27

Rewrite g(x) using b = 27 and the same slope, m = 12.

g(x) = 12x + 27

7 0
3 years ago
Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her
Art [367]

For this case we have the following equation:


y + 1 = 2 (x - 3)

That can be rewritten in the form y = mx + b

Where:


  • m is the slope of the line
  • b is the cut point

So, we have:


y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7

Where:


m = 2 is the slope


b = -7 is the cut point


Carlota has the following points:


(-1, 3) and (2, 9)


To know if the line y = 2x-7 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:


Point (-1, 3):


Substituting:


3 = 2 (-1) -7\\3 = -2-7

3 = -9 It's false, equality is not met. The point (-1, 3) does not go through the line.


The equation written by Carlota is erroneous, the procedure to follow is:


Given(x1, y1) = (- 1, 3) and(x2, y2) = (2, 9), we find the slope:


m=\frac{(y2-y1)}{(x2-x1)}

m=\frac{(9-3)}{(2-(-1))}

m=\frac{6}{3}

m=2

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:


y = 2x + b

Substituting (2,9) we have:


9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is y = 2x + 5

Answer:


The correct equation of the line that passes through the given points is y = 2x + 5

Carlota's mistake was at the cutoff point


5 0
2 years ago
HELP PLEASE asap I behind
Evgen [1.6K]
126 + 9x = 180
180 - 126 = 54
9x = 54
x = 6

mark me brainliest if the answer is correct , thank you in advance :)
4 0
3 years ago
2. The volume of both of these trapezoidal prisms is 24 cubic units. Their
Valentin [98]

Answer:

area of a trapezoidal base  of each prism with heights  6 and 8 units are 4 square units and 3 square units respectively

Step-by-step explanation:

Let us first be aware of formula of volume for any regular geometrical figure.

Fundamental formula for  volume for any regular geometrical figure is.

volume = area of cross section of object*  height of object (A)

In the problem stated area of cross section of object will be  area of a trapezoidal base.

Given in the question is

Volume of both the trapezoidal prisms = 24 cubic units

*************************************************************************************

For prism with height 6 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 6 * area of a trapezoidal base

=> area of a trapezoidal base = 24/6 = 4 square units

*************************************************************************************

For prism with height 8 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 8 * area of a trapezoidal base

=> area of a trapezoidal base = 24/8 = 3 square units

*************************************************************************************

Therefore area of a trapezoidal base  of each prism with heights  6 and 8 units are 4 square units and 3 square units respectively.

4 0
3 years ago
Solve 3x − 2 = 37. please help me
lyudmila [28]

Answer:

x=13

Step-by-step explanation:

1. Isolate the variable

3x - 2 = 37

     +2 = +2

2. Divide the equation by the coefficient

3x = 39

/3    /3

3. Answer

x = 13

8 0
3 years ago
Read 2 more answers
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