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miss Akunina [59]

3 years ago

13

Is the set of integers closed under division?

1 answer:

Gnesinka [82]3 years ago

5 0

No there not it can even be converted into a a decimal and fractions

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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

3 years ago

Find the Domain and Range of the graph<br> Plz helppppppppppp

Semenov [28]

Domain: 1 2 3 4 5 6 range: -1 0 1 2 3 6

3 0

3 years ago

Read 2 more answers

Two lines that intersect to form right angle are called

Sergio039 [100]

Answer:

perpendicular

Step-by-step explanation:

When 2 lines intersect at any point, not just in the middle of each (that has nothing to do with it), and they meet to form right angles, the lines are perpendicular to one another and their slopes are opposite reciprocals.

4 0

3 years ago

Bob ran 7 times a week for a number of weeks what is the algebraic phrases

34kurt

Answer:

I'd assume 7 times x, or 7x

Step-by-step explanation:

Algebraic phrases don’t include the equal sign and based on the information you gave me, I think 7x is the answer.

8 0

3 years ago

please help im trying to get answers but people just putting silly comments on my questions please please give me a hand all in

ankoles [38]

Answer:

8 ================================================================ D

i might be incompetent but at least I'm not impotent

Step-by-step explanation:

3 0

3 years ago