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expeople1 [14]
3 years ago
15

“encontrar la integral indefinida y verificar el resultado mediante derivación”

Mathematics
1 answer:
Oliga [24]3 years ago
4 0

I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx

Haz la sustitución:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C

Para confirmar el resultado:

\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}

I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx

Sustituye:

y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx

\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C

(Te dejaré confirmar por ti mismo.)

I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx

Sustituye:

y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx

\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C

I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}

Sustituye:

u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}

\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C

Podemos hacer que esto se vea un poco mejor:

\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}

\implies I=-\dfrac{(t+1)^4}{4t^4}+C

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4. The student council sold flowers for the Sweetheart dance as a fundraising
vekshin1

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Total flowers sold = 200

Flowers are :

Carnations, Roses, and Gerber daisies

Carnations = c

Roses = r

Daisies = d

20 fewer roses than daisies ; r = d - 20

Total sales = $453

c = $1.50 each ; r = 3.75 each ; d = 2.25 each

c + d + d - 20 = 200

c + 2d = 220 - - (1)

1.50c + (d - 20)(3.75) + 2.25d = 453

1.50c + 3.75d - 75 + 2.25d = 453

1.50c + 6d = 528 - - - (2)

From (1)

c = 220 - 2d

1.5(220 - 2d) + 6d = 528

330 - 3d + 6d = 528

330 + 3d = 528

3d = 528 - 330

d = 198/3

d = 66

66 × 2.25 = $148.5

c = 220 - 2(66)

c = 88

88 * 1.50 = $132

r = d - 20

r = 66 - 20

r = 46

46 × $3.75 = $172.5

8 0
3 years ago
The mean age and median age of 6 people in a room is 40 years. a person whose age is 60 years leaves the room. question 1. if po
FromTheMoon [43]
Mean = (total of contributors) / (number of contributors)

For the 6 people in the room, you have
   40 = (total of contributors) / 6
   (total of contributors) = 6*40 = 240

A 60-year-old left the room, decreasing the total of contributors by 60.
   (new total of contributors) = (total of contributors) - 60
   (new total of contributors) = 240 - 60 = 180

Then the new mean is
   (new mean) = (new total of contributors) / (new number of contributors)
   (new mean) = 180 / 6 = 36

The mean age of the remaining 5 people is 36.
3 0
3 years ago
Is the answer C ; y= -3x-1
Sonja [21]

Answer:

I believe you are correct

Hope This Helps!      Have A Nice Day!!

8 0
3 years ago
Read 2 more answers
60 points!!! pls help
Tasya [4]

Answer:

im answering so the other guy can get brainliest...

hv a great day!!! :)

Step-by-step explanation:

5 0
2 years ago
A spherical globe has a diameter of 10 inches. What is the approximate volume of the globe?
adelina 88 [10]

Answer:

523.33 in^3

Step-by-step explanation:

A sphere is a 3-dimensional version of a circle. An example of a sphere is a ball

Volume of a sphere = \frac{4}{3}πr^{3}

Where

π = 3.14

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

diameter = 2r

Radius = 10 in / 2 = 5 inches

\frac{4}{3} × 3.14 ×5^{3} = 523.33 in^{3}

6 0
3 years ago
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