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3 years ago

11

Hello can anyone help me with this one questions?

1 answer:

zysi [14]3 years ago

3 0

Answer: c

Step-by-step explanation:

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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

At the start of the softball season, the p players on the Hammerin' Homers softball team each

Lapatulllka [165]

(18*7)+(20*10) * means times

8 0

3 years ago

What is 50 divided by 48 in all kinds of forms

galben [10]

You put it 48 divide 50 which equally 0.96 or 50 divide 48 which equal 1.04166666667

7 0

3 years ago

What is 6 qt 15 fl oz - 4 pt 4 fl oz =____pt____fl oz

yan [13]

Answer:

4.0 = 64. 5.0 = 80. pints to fluid ounces. 6.0 = 96. 7.0 = 112. 8.0 = 128. 9.0 = 144. 10 = 160. 1 US fluid ounce ( fl oz) = 0.0625 US pints ( pt) = 0.03125 US quarts (qt) = 0.125 US cups (c) = 6 US teaspoons = 2 US tablespoons = 29.5735296 milliliters (ml) = 0.0295735296 liters (l).

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

| f − 6 | = | f + 8 |

ikadub [295]

Answer:

f = - 1

Step-by-step explanation:

f - 6 = f + 8

f - 6 = - (f + 8)

f ∈ ∅

f - 6 = - (f + 8)

8 0

3 years ago