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Mekhanik [1.2K]
3 years ago
15

Calculate the area under the graph of f(x) = 1/xlnx from x = e to x = e^e

Mathematics
1 answer:
Gnom [1K]3 years ago
7 0

Using integration, it is found that the area under the graph of f(x) in the desired interval is of 1 unit squared.

<h3>How is the area under a graph found?</h3>

The area under the graph of a curve f(x) between x = a and x = b is given by the following integral:

A = \int_{a}^{b} f(x) dx

In this problem, the function and the limits of integration are given by:

f(x) = \frac{1}{x\ln{x}}

a = e, b = e^e

Hence:

A = \int_{e}^{e^e} \frac{1}{x\ln{x}} dx

Using substitution:

u = \ln{x}

du = \frac{1}{x} dx

dx = x du

Hence:

\int \frac{1}{x\ln{x}} dx = \int \frac{1}{u} du = \ln{u} = \ln{\ln{x}}

Applying the Fundamental Theorem of Calculus:

A = \ln{\ln{e^e}} - \ln{\ln{e}} = \ln{e\ln{e}} = \ln{\ln{e}} = \ln{e} - \ln{1} = 1

Hence, the area under the graph of f(x) in the desired interval is of 1 unit squared.

To learn more about integration, you can take a look at brainly.com/question/20733870

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Find the area of the polygon with the given vertices. J(-3,4), K(4,4), L(3,-3)
Margarita [4]

Answer:

<h2>             A = 24.5 square units</h2>

Step-by-step explanation:

J(-3,\,4)\ \ \implies\ y_J=4\\\\K(4,\,4)\ \ \implies\ y_K=4\\\\y_K=y_J\ \ \implies\ JK\parallel X{-}axis\ \implies\ H=|y_L-y_K|\quad\ \{for\ JK=base\}\\\\H=|-3-4|=|-7|=7\\\\\\ JK\parallel X{-}axis\ \implies\ B=JK=|x_J-x_K|=|-3-4|=7\\\\\\A=\frac12BH\\\\A=\frac12\cdot7\cdot7=24.5

                     

3 0
3 years ago
a landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 sq
Blizzard [7]
<span>As for this problem, we will first establish that the length of the flower bed be represented as x, the width of the flower bed be represented as x/2 ,and the area of the flower bed be taken as it is since it is given. We then follow the formula for area which is length multiplied to width which is:<span>
A = LW

we then substitute them

34 square feet = x (x/2)
now all we need to do is find x first.

34 square feet = x squared / 2
now do a cross multiplication

68 square feet = x squared
then get the square root of both sides

8.246 feet = x

Since x is equal to the length of the flower bed, all we have to do to get the width of it is to divide it by 2. So...

W = x/2
W = 8.246 feet / 2
W = 4.123 feet

<span>And since the problem asked it to find the width of the flower bed to the nearest tenth of a foot, the answer would be 4.1 ft.</span></span></span>
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3 years ago
Find The Quoteint Plz Help
Arisa [49]
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6 0
3 years ago
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Part of the graph of the function f(x) = (x + 4) (x - 6) is shown below. A 2 Which statements about the function are truc? Selec
jonny [76]

The true options include the following:

  • The vertex of the function is at (1,–25).
  • The graph is negative on the entire interval –4 < x < 6.

<h3>What is a Graph?</h3>

This is defined as a pictorial representation of data or variables in an organized manner.

Function f(x) = (x + 4)(x – 6)

Graph intersects the x-axis at points (-4,0) and (6,0).

x-coordinate of vertex = -4+6/2 = 1

y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25

The vertex is at the point (1,-25).

The graph is positive for all x< -4 or x>6.

The graph is negative for –4 < x < 6.

Read more about Graph here brainly.com/question/19040584

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4 0
2 years ago
You are mowing your neighbor's lawn. He is going to pay you $20.00 for the first two hours and $5.00 for anything after that. Wh
slamgirl [31]

Answer:

D. 20 +5(h - 2)

Step-by-step explanation:

This equation represent this problem because you are paid $5 an hour AFTER the first hour because you were paid an initial $20 for the first two hours.

8 0
3 years ago
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