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-   -   Need help with an integral (https://www.mersenneforum.org/showthread.php?t=15511)

Baztardo 2011-04-10 13:44

Need help with an integral
 
Hi there! New to this forum and not good at math.. I wonder if anyone of you could help me with this matter?


The Integrand is:

pi (t-6)
P(t)= A sin _______ +B
12


The Integral is:

a

/
| P(t)dt
/

b


The following facts are known:

A=0.56
B=0.28
a=4
b=20

Thank you guys!

/Baz

Christenson 2011-04-10 15:48

I don't understand P(t), which I believe to be A * sin( X ) + B, where X is (t*pi-6)/12. Please confirm, also confirm that your interval of integration (a to b) is going backwards, that is, a > b, so dt is negative. Once we have that, the result will be straightforward.

Baztardo 2011-04-10 19:12

Hi there!

It´s pretty hard for me to explain. Perhaps I missplaced this question. I havent been to school for ages and I´m trying to solve this one in order to get som coordinates. I could explain the original problem:

The formula above is edited by a person trying to solve it. Perhaps your more helped by the one originally made?

pi (t-6)
P(t)= A sin +B
12

b
/
| P (t)
/
a

As before:

A = 0,56
B = 0,28
a = 4
b = 20

I have this facts:

N 57 43.Y00
E 012 54.X6Y

By solving above integral Y and X should appear.

The answer to the matter is a decimalnumber where Y is the numbers after the decimal "roughly". And X is half the number before the decimal.

Englisg is myc second languagae, I hope you understand a little more than before :)

Mathew 2011-04-10 19:56

[TEX]\int_{b}^aA\sin\left(\frac{\pi(t-6)}{12}\right)+B dt[/TEX] what I understood from Baz's post


[TEX]\int_{a}^bA\sin\left(\frac{t\pi-6}{12}\right)+B dt[/TEX] what Christenson wrote

Let us look at Christenson's equation without the points

[TEX]\int_{}A\sin\left(\frac{t\pi-6}{12}\right)+Bdt[/TEX]

Break this into two integrals

[TEX]\int_{}A\sin\left(\frac{t\pi-6}{12}\right)dt+\int_{}Bdt[/TEX]

Let us do the harder integral first

[TEX]\int_{}A\sin\left(\frac{t\pi-6}{12}\right)dt[/TEX]

A is a constant and can be placed outside of the integral

[TEX]A\int_{}\sin\left(\frac{t\pi-6}{12}\right)dt[/TEX]

Next is an u-substitution

let [TEX]u=\frac{t\pi-6}{12}[/TEX]

then [TEX]du=\frac{\pi}{12}dt[/TEX]

Therefore [TEX]dt=\frac{12}{\pi}du[/TEX]

Substitute the values

[TEX]A\int_{}\frac{12}{\pi}\sin\left(u\right)du[/TEX]

Again since [TEX]\frac{12}{\pi}[/TEX] is a constant move it out of the integral

Now you have

[TEX]A\frac{12}{\pi}\int_{}\sin\left(u\right)du[/TEX]

Which is

[TEX]-A\frac{12}{\pi}\cos\left(u\right)[/TEX]

replace the u for what was substituted

[TEX]-A\frac{12}{\pi}\cos\left(\frac{t\pi-6}{12}\right)[/TEX]

Now do the second integral

[TEX]\int_{}Bdt =Bt[/TEX]

The whole equation is

[TEX]-A\frac{12}{\pi}\cos\left(\frac{t\pi-6}{12}\right)+Bt[/TEX]

Evaluating from a to b i.e. [TEX]\int_{a}^b[/TEX] it would be the following

[TEX]\left(-A\frac{12}{\pi}\cos\left(\frac{b\pi-6}{12}\right)+B*b \right)-\left(-A\frac{12}{\pi}\cos\left(\frac{a\pi-6}{12}\right)+B*a\right)[/TEX]

Entering in all the values =6.25624

Batalov 2011-04-10 20:28

In 'Homework Help' forum, the usual thing to do would be to give [I]hints[/I], not a complete solution. One doesn't learn anything by simply copying the solution and turning it in.

Baztardo 2011-04-10 20:47

Thanks!
 
Thank you so much for helping me out with this one Mathew!!

And as a respond to moderator. I wrote above that this might be places in wrong forum since i dont intend learning the steps from the answer, this is way way way beyond my current skills in mathematics. And second it wasn´t a homework task, rather some problemsolving task inside the geocaching community.

Best wishes all of you!

/Baz

Christenson 2011-04-10 22:17

In Baz' defense, he did state that he wasn't doing homework in the classical sense. Mr Stene, thanks for the nice formatting.

Batalov, is my number theory homework, given to me by R.D Silverman (reading the literature and ensuring that I actually understand it, no grading involved) more appropriate here or under Factoring? I'm thinking about things like incremental QS, which may or may not work.


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