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3 years ago

10

"For each power, write an equivalent multiplication expression with two factors"

1 answer:

Eva8 [605]3 years ago

3 0

<h2>10⁴ = 10²⁺² = 10² × 10² </h2><h2>8² = 8¹⁺¹ = 8¹ × 8¹ </h2><h2 /><h2 />

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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

A, b, c or d?????? Pls help quick

Georgia [21]

Answer:

The answer is a

Step-by-step explanation:

have a nice day :)

5 0

3 years ago

Write an equation of the line below.

Blizzard [7]

Answer:

y=1/2x+4

Step-by-step explanation:

Refer to the picture that given :)

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3 years ago

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When –9x” is divided by –3x3, x = 0, the quotient is

iragen [17]

Answer:

0

Step-by-step explanation:

-9 x 0 is 0 and dividing anything with 0 is 0

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4 years ago

I won $60,000 I invested part in a CD at 2% interest the rest at 3%interest in a cd at the end of the year I earned $1600 in int

zaharov [31]

Let x = amount invested in 2% CD and y = amount invested in 3% CD
x + y = 60000
0.02x + 0.03y = 1600
SOLVE THE 1st EQUATION FOR x AND SUBSTITUTE RESULT IN 2nd
0.02(60000 - y) + 0.03y = 1600
1200 - 0.02y + 0.03y = 1600
0.03y = 400
y = 13333.34
x = 46666.66

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3 years ago

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