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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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galina1969 [7]
Fine increase = 78 - 65 = 13
Increase rate = 13/65 x 100% = 20%

Discounted amount = 560 - 476 = 84
Discount rate = 84 / 560 x 100% = 15%
5 0
3 years ago
The sum of Alan’s age and Bob’s age is 40.
Nutka1998 [239]
Carl is 2 yrs older than bob. Because Alan+Carl is 2 more than Alan+bob
So bob=16 and Carl is 18
16+18=34
And Alan is 24
8 0
3 years ago
If the height is 24, solve for x. h=-16x^2+8x+48
disa [49]

Answer:

x=  

32

7+  

3121

​  

 

​  

,  

32

7−  

3121

​  

 

​  

 

Step-by-step explanation:

h+16^2-8x-48=0

-7x+16x^2-48=0

x=  

32

7+  

3121

​  

 

​  

,  

32

7−  

3121

​  

 

​  

 

8 0
2 years ago
I) Consider the following figure,<br><br> ​<br><br> ​<br><br> ​
qwelly [4]

Step-by-step explanation:

If PQRS is a quadrilateral inscribed in a circle, then the opposite angles of the quadrilateral are <u>supplementary</u><u>.</u>

y + 68° = 180° { being opposite angles of cyclic quadrilateral }

y = 180° - 68°

y = 112°

x + 82° = 180° { being opposite angles of cyclic quadrilateral }

x = 180° - 82°

x = 98°

Hope it will help :)❤

4 0
2 years ago
Please help me with this ​
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345235235232352352353523523535

5 0
3 years ago
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