Given the function below, identify the statements that are correct: *

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

Oliga [24]

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

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:

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

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

4 0

3 years ago

Marcus changed jobs after college. His old salary was $48000 per year. Now his new salary is 37% more per year. What is his new

Gennadij [26K]

Answer:

65,760

Step-by-step explanation:

5 0

3 years ago

Don’t know how it looks hope it’s better

sveticcg [70]

Answer:

80 ounces

Step-by-step explanation:

In one pint, there is 16 ounces. Thus, if she picked five pints, 16 × 5 = 80 ounces.

Another way to solve this problem is by setting a proportion.

$\frac{2cups}{1pint} = \frac{10cups}{5pints}$
$\frac{8ounces}{1cup} \frac{80ounces}{10cups}$

Therefore, the answer is 80 ounces.

3 0

2 years ago

Please help me solve this I need some help

Agata [3.3K]

Answer:

f = 8

Step-by-step explanation:

Apply the distributed property, so it now looks like this: 2f - 10 = 6
Add 10 to each side, so it now looks like this: 2f = 16
Divide each side by 2 to cancel out the 2 next to f. It should now look like this: f = 8

I hope this helps!

7 0

3 years ago

Read 2 more answers

In a population of grasshoppers, the ratio of grasshoppers with a white marking to those without a white marking is 2:3. An ento

LekaFEV [45]

Answer:

D. 116

Step-by-step explanation:

Let the grasshoppers with a white marking be 2x.

Let the grasshoppers without a white marking be 3x.

2x + 3x = 290

5x = 290

x = 290 / 5

x = 58

The grasshoppers with a white marking

= 2x

= 2 ( 58 )

= 116

3 0

3 years ago