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2 years ago

Can anybody check and see if 11 and 12 are correct. I will Give Brainliest Answer.

Mathematics

1 answer:

iogann1982 [59]2 years ago

8 0

11 is correct, i did 12 and you did it correctly

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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

Please help ASAP please and thank you have a great and blessed day!

goldenfox [79]

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3 0

3 years ago

Read 2 more answers

Why would someone want to factor a polynomial? Provide real-world examples of different questions we can answer or factors we ca

IgorC [24]

Factoring is a common mathematical process used to break down the factors, or numbers, that multiply together to form another number. Some numbers have multiple factors.

<u>Explanation:</u>

Factoring polynomials involves breaking up a polynomial into simpler terms (the factors) such that when the terms are multiplied together they equal the original polynomial. Factoring helps solve complex equations so they are easier to work with. Factoring polynomials includes: Finding the greatest common factor.

Factoring (called "Factorizing" in the UK) is the process of finding the factors: Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

6 0

3 years ago

Factor the following using GCF and show work. 6x^2+42x-18

aniked [119]

The greatest common factor is 6. Thus means we divide every part of the expression by 6.

6x^2/6 = x^2
42x/6 = 7x
-18/6 = -3

Your new expression is 6(x^2 + 7x -3).

8 0

2 years ago

Need help with this math question <br>will give 5 stars and mark best<br>

Stolb23 [73]

I used similarities in triangles

5 0

2 years ago