Any idea on this wrong integral method?

John E. Franklin · 2010-04-24 08:30:13

Say you take a curve of some form,
and start somewhere on it, and start
adding up columns of area (rectangles of thin x),
and keep summing to the right.
Why would this total not draw the correct integral?
I don't know why or where I thought it up?
But it doesn't work for a sine wave.
For a sine wave, the -cosine result doesn't
come up, instead we get a wavelength
double the size I think.
Anyone know where this crazy idea came from?
Or if it can be modified to work?

bobbym · 2010-04-24 12:12:48

Hi John;

Do you mean this?

John E. Franklin · 2010-04-25 08:45:55

Yes note that the total summing area keeps going upward for that x up to pi.
So maybe this method is only good for definite integrals, not for the equation form,
since the wavelength would come out twice as long I think.

bobbym · 2010-04-25 09:26:32

Hi John;

As you force more and thinner rectangles underneath that curve you will approximate the Area better and better. When you put an infinite amount of rectangles underneath you get the area exactly,

John E. Franklin · 2010-05-03 06:16:26

I'm not doing a definate integral for area though.
I'm trying to get the integral equation.
And the method I'm using is false, and made-up, probably from the derivative methods that were taught to me.

bobbym · 2010-05-03 13:29:42

Hi John;

How about an example. Right or wrong who cares?

John E. Franklin · 2010-05-03 20:23:15

Well okay, I don't know if I can do it. I was doing an approximate idea in my head for the sine wave, so
I'll stick to that first. Add up the area of the first 1/2 of a sine wave and it keeps going positive. So now
this new plot is something with positivie slope but curvy. Then along comes the 2nd half of a sine wave,
and the area goes negative, so this summation drags the new curve with a negative slope, back to the
x-axis at 360 degrees, so now I'll try to plot it by guessing for now. Later, I might program this to
get a better picture with BASIC. Actually, it might have the same wavelength as the original curve, just
pushed above the x-axis, instead of going above and below the x-axis.

Last edited by John E. Franklin (2010-05-03 20:34:49)

bobbym · 2010-05-03 20:37:32

Hi John;

Burning the midnight oil? I know I am a barbarian but when you talk about stuffing rectangles under some curve, I think we are discussing definite integration, Indefinite integration is the inverse operator of differentiation. Now how are going to get the inverse of differentiation by stuffing rectangles underneath a curve? What comes next?

JaneFairfax · 2010-05-04 09:37:33

John E. Franklin wrote:

For a sine wave, the -cosine result doesn't
come up

Whats the problem?

JaneFairfax · 2010-05-04 10:06:56

If youre finding area by integrating between 0 and a general x > 0, you must take the modulus of the integrand.

Last edited by JaneFairfax (2010-05-04 10:13:39)

ZHero · 2010-05-04 14:40:53

JaneFairfax wrote:

John E. Franklin wrote:
For a sine wave, the -cosine result doesn't
come up
Whats the problem?

I guess, he means to say that when u add all the small rectangles of the sine wave then you get a sine wave which has double the wavelength, instead of getting the cosine wave!
can u GRAPHICALLY SHOW How and Why is the Integration of sine wave is a Cosine wave??

bobbym · 2010-05-04 17:47:54

bobbym wrote:

Now how are going to get the inverse of differentiation by stuffing rectangles underneath a curve?

Post # 10 has a really nice formula. From my interpretation of big John's post, he is trying to get something like that but using rectangles. That is what I don't see how to do. Sorry I was unclear.

ZHero · 2010-05-04 18:02:13

JaneFairfax wrote:

John E. Franklin wrote:
For a sine wave, the -cosine result doesn't
come up
Whats the problem?

ok.. i see...

and i guess this can give you the required graph...
however.. i'm not really sure!

Last edited by ZHero (2010-05-04 18:03:35)

MathsIsFun · 2010-05-05 09:29:35

[Deleted a conversation that got out of hand]

For future reference: bobbym is a Moderator, please let his decisions stand.

John E. Franklin · 2010-05-05 20:29:34

When I get the time, I'll program the rectangles method to get an integral equation of another curve.
The method idea is simple, but I don't know if it is wrong or right. Simply for any point you are plotting
your integral equation, you simply are doing a definate integral from the leftmost starting point to this
point of interest. So I plan to just move along from left to right and make a plot. But I am quite busy
now with my Dad's stroke and taking care of him. He has to regain his balance and walk again...

bobbym · 2010-05-05 20:37:02

Hi John;

Sorry to hear about that. I hope he will.

John E. Franklin · 2010-05-10 14:32:24

Thanks bobby!
Without doing any programming yet, I am pretty well convinced by Janes post # 9 that the rectangle
method will work just as the integral she shows there in that post # 9.
Someday, I'll program the approximation graph for fun...
Because Janes 0 to x is like my summation to that point from left to right...

bobbym · 2010-05-10 15:00:15

Hi John;

So, Jane did have a good perspective on it. As she seems to have done what you wanted.

J Bernoulli wrote:

"I recognize the lion by his paw"

John E. Franklin · 2010-05-12 05:26:45

Yes Indeed! Jane is amazing.

bobbym · 2010-05-12 05:28:25

That will certainly brighten up her day. How is your Dad doing?

Math Is Fun Forum

#1 2010-04-24 08:30:13

Any idea on this wrong integral method?

#2 2010-04-24 12:12:48

Re: Any idea on this wrong integral method?

#3 2010-04-25 08:45:55

Re: Any idea on this wrong integral method?

#4 2010-04-25 09:26:32

Re: Any idea on this wrong integral method?

#5 2010-05-03 06:16:26

Re: Any idea on this wrong integral method?

#6 2010-05-03 13:29:42

Re: Any idea on this wrong integral method?

#7 2010-05-03 20:23:15

Re: Any idea on this wrong integral method?

#8 2010-05-03 20:37:32

Re: Any idea on this wrong integral method?

#9 2010-05-04 09:37:33

Re: Any idea on this wrong integral method?

#10 2010-05-04 10:06:56

Re: Any idea on this wrong integral method?

#11 2010-05-04 14:40:53

Re: Any idea on this wrong integral method?

#12 2010-05-04 17:47:54

Re: Any idea on this wrong integral method?

#13 2010-05-04 18:02:13

Re: Any idea on this wrong integral method?

#14 2010-05-05 09:29:35

Re: Any idea on this wrong integral method?

#15 2010-05-05 20:29:34

Re: Any idea on this wrong integral method?

#16 2010-05-05 20:37:02

Re: Any idea on this wrong integral method?

#17 2010-05-10 14:32:24

Re: Any idea on this wrong integral method?

#18 2010-05-10 15:00:15

Re: Any idea on this wrong integral method?

#19 2010-05-12 05:26:45

Re: Any idea on this wrong integral method?

#20 2010-05-12 05:28:25

Re: Any idea on this wrong integral method?

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