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ahrayia [7]
2 years ago
9

Haya la integral de xarcsenx/((1-x^2)^1/2). Utiliza la sustitución de t= arcsenx

Mathematics
1 answer:
ikadub [295]2 years ago
7 0

Answer:

<em>Explicación más abajo</em>

Step-by-step explanation:

Integración Indefinida

La integral

I=\int \dfrac{x .arcsen\left(x\right)}{\sqrt{1-x^2}}

Se resuelve con el cambio de variables:

t=arcsen(x)

Una vez hechos los cambios, la integral se resuelve en función de t:

I=sen(t)-t.cos(t)+C

Hay que devolver los cambios para mostrarla en función de x.

El cambio de variables también se puede escribir:

x=sen(t)

Recordando que

cos(t)=\sqrt{1-sen^2(t)}

Entonces:

cos(t)=\sqrt{1-x^2}

Devolviendo los cambios:

I=sen(t)-t.cos(t)+C=x-arcsen(x)\sqrt{1-x^2}+C

Es la respuesta correcta

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The bowling alley and the swimming pool both offer birthday party rentals the bowling alley coast $5 per person plus a $15 room
Vanyuwa [196]

Answer:

Swimming pool

Step-by-step explanation:

Let's say that we invite x people. The cost of the bowling alley will be $15 for the room, and we add $5 dollars for each person. Therefore, we can represent the cost of the bowling alley as

5 * x + 15

Similarly, the cost of the swimming pool is

4 * x + 12

To find the maximum of the function, one thing we can do is set the expressions of the cost equal to 40. This will give us the amount of people we can invite for exactly 40 dollars. Because cost increases with amount of people, this will give us the maximum number of people we can invite with $40.

We thus have

5 * x+ 15  = 40

subtract 15 from both sides to isolate the x and its coefficient

25 = 5 * x

divide both sides by 5 to isolate x

25/5 = x = 5

We can therefore invite 5 people to the bowling alley

4 * x+ 12  = 40

subtract both sides by 12 to isolate the x and its coefficient

28 = 4 * x

divide both sides by 4 to isolate x

x = 7

Therefore, we can invite 7 people to the swimming pool. As 7 > 5, we can invite more people to the swimming pool.

A quicker way to solve this could be by looking at the cost of each location. Because the bowling alley costs more both per person and for the room, and there is no way to decrease the cost except by decreasing the amount of people, there is no way that the bowling alley could get as many people as the swimming pool with the same amount of money

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2 years ago
Find the area of a rectangle with side lengths 3/5 inch and 5/6 inch
Helga [31]

Answer:

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Step-by-step explanation:

You multiply the fractions

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2 years ago
Reciprocal of 12 by 15 is​
romanna [79]

the reciprocal is 15 by 12

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3 years ago
If i have 100 gummy vitamins and i take two a day how many months would they last me?
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2 years ago
I’m so confused on how to do this
dimaraw [331]

Answer:

19

Step-by-step explanation:

First:  Recognize that (f o g)(x) is the "composition" of two functions, where g(x) serves as the input to f(x).  We are given f(x) = 2x+3 and g(x) = x+5.  You could find g(3) right now:  it is g(3) = 3+5 = 8.  Use this 8 as the input to f(x):  f(8) = 2(8)+3 = 19.

3 0
3 years ago
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