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2 years ago

Simplify

Mathematics

1 answer:

bazaltina [42]2 years ago

4 0

The answer I got is 17x-70/5

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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

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

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

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

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

6 0

2 years ago

How many times larger then 2x10² is 2x10⁸

Brrunno [24]

Answer:

1,000,000 times larger

Step-by-step explanation:

2 x $10^{8}$ = 200,000,000

2 x $10^{2}$ = 200

200,000,000 divided by 200 is 1,000,000

It can also be solved by subtracting the exponents from 10. Then dividing the two number being put the scientific notation.

$10^{8} - 10^{2}$ = $10^{6$

2 ÷ 2 = 1

Now solve:

1 x $10^{6$ = 1,000,000

3 0

3 years ago

What is the value of x? round the answer to the nearest tenth. the diagram is not drawn to scale.

Zepler [3.9K]

It would also be 60°
B

8 0

3 years ago

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What is the product of 9 and -7?

kolezko [41]

Answer:

The product of 9 and -7 is -63

Step-by-step explanation:

Hope This Helped!

3 0

3 years ago

What if the 360 cubic-inch paving stones are 4 inches thick and any whole number length and width are possible? How many differe

AleksAgata [21]

Umm im gonna guess on this one because im not good at math lol
, 3.58?

6 0

3 years ago

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