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2 years ago

Pleas I need help now

Mathematics

1 answer:

Zina [86]2 years ago

8 0

I can't see the picture it is too small

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Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

2 years ago

You need a loan of $135,000 to buy a home. Calculate your monthly payment and total closing costs for each choice below. Briefly

Ahat [919]

You need to multiply the four numbers and then takeway

6 0

3 years ago

PLZZZZZZZZZZZZZZ help

amm1812

Answer:

Step-by-step explanation:

18 -15 = 3

3 0

2 years ago

Read 2 more answers

if the variance of the data values in a population is 256, what is the standard deviation of the data values?

kumpel [21]

The standard deviation is the square root of the variance

so if the variance is 256, then the standard deviation is : sqrt 256 = 16 <==

5 0

3 years ago

This recipe makes a cake big enough to serve 4 people.

nignag [31]

Answer:

He can make a cake that serves 24 people.

Step-by-step explanation:

Gareth has 13 eggs, but only 2 are needed for 4 servings. 13 divided by 2 equals 6.5. We can't serve half of a person, so there will be a large cake equivalent to the size of 6 small cakes. Since 1 small cake serves 4 people, and Gareth's large cake is 6 times the size of a small cake, Gareth's cake can serve a total of 24 people. Now that is one big cake!

P.S. If you found this answer helpful, please mark me as Brainliest

7 0

2 years ago