3 years ago

Need help with square problem

Mathematics

1 answer:

katrin2010 [14]3 years ago

5 0

Answer:

Step-by-step explanation:

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Why is the answer to this integral's denominator have 1+pi^2

ss7ja [257]

It comes from integrating by parts twice. Let

$I = \displaystyle \int e^n \sin(\pi n) \, dn$

Recall the IBP formula,

$\displaystyle \int u \, dv = uv - \int v \, du$

Let

$u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Then

$\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn$

Apply IBP once more, with

$u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Notice that the ∫ v du term contains the original integral, so that

$\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)$

$\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I$

$\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n$

$\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C$

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2 years ago

A kitchen makes 2,944 ounces of soup each week. There are 128 ounces in 1 gallon. How many gallons of soup does the kitchen make

Rashid [163]

I calculated its 14 gallons is in two week
1 gall=128
128 x 1st week= 896
128 x 2nd week=1792divid it by 128=14
mark me as brainlest

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3 years ago

HELPPP! I’ll mark Brainliest (NO joke answers)

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jk, the answer is 3

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Alternate Interior Angles. You’re welcome

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2 years ago

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Need help with square problem​

Need help with square problem