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kherson [118]
3 years ago
7

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
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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
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Answer: benis

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