cooldudeman
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I have no idea how to do this because I got the wrong answer. What I did made sense to me but its completely wrong according to the solutions.

Q7

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TeeEm
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(Original post by cooldudeman)
I have no idea how to do this because I got the wrong answer. What I did made sense to me but its completely wrong according to the solutions.

Q7

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stupid question

firstly the region is the first two bounded regions of sinx, between x = 0 and x =2pi
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cooldudeman
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(Original post by TeeEm)
stupid question

firstly the region is the first two bounded regions of sinx, between x = 0 and x =2pi
Oh yeah my bad. My answer would change to -1<y<1

So my answer is finding all if the sinx regions from 0 to infinity. I dont know how to limit it to 0 to 2pi

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TeeEm
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(Original post by cooldudeman)
Oh yeah my bad. My answer would change to -1<y<1

So my answer is finding all if the sinx regions from 0 to infinity. I dont know how to limit it to 0 to 2pi

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I think also it is not arcsin for the whole region
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atsruser
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(Original post by cooldudeman)
I have no idea how to do this because I got the wrong answer. What I did made sense to me but its completely wrong according to the solutions.

Q7

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It looks to me that you are integrating over all of the area defined by y=\sin x for x \in [0,2\pi] so when you swap order the limits on x for the first chunk will look like:

\int_{x=\arcsin y}^{x=?} f(x,y) dx

where you need to choose ? to make a line segment parallel to the x-axis inside the sine curve, bordered by the left hand limit in [0,90] and the right hand limit in [90,180]. (Yeah, I know - poor description - sorry) I'll leave the rest to you.

I don't think this can be done without splitting up the integral; maybe that's what TeeEm means by "stupid"?
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TeeEm
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(Original post by cooldudeman)
Oh yeah my bad. My answer would change to -1<y<1

So my answer is finding all if the sinx regions from 0 to infinity. I dont know how to limit it to 0 to 2pi

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I made a question for my own use, to explain your one...

I have not typed it yet so you are looking at the solution.

IMG.pdf

part (a)
Integrate 4y over the the region bounded by y = sinx, from 0 to π
this is very easy

next part (b)
verify the answer of part (a) by reversing the limits


your integral has to be split 4 ways!!!

from x = arcsiny to x = π/2, y = 0 to y=1
from x= π/2 to x = π - arcsiny, y = 0 to y=1
from x = π - arcsiny to x =3π/2, y = 0 to y=-1
from x =3π/2 to x = 2π + arcsiny, y = 0 to y=-1
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atsruser
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(Original post by TeeEm)

your integral has to be split 4 ways!!!
I thought it can be done in 2, but it's too late for me to work through: \arcsin y to \pi - \arcsin y for the +ve chunk etc?
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TeeEm
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(Original post by atsruser)
I thought it can be done in 2, but it's too late for me to work through: \arcsin y to \pi - \arcsin y for the +ve chunk etc?
possibly it can be done (depending on the integrand) by using some symmetries which at the moment my brain cannot handle ...

in all cases this question with an actual integrand (even as simple as mine, and with half the region) is a joke.

I guess all it is required in the exercise is to show the general expression for 4 integrals of f(x,y) with the limits I am giving (I hope no mistakes on my part)
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TeeEm
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(Original post by cooldudeman)
Oh yeah my bad. My answer would change to -1<y<1

So my answer is finding all if the sinx regions from 0 to infinity. I dont know how to limit it to 0 to 2pi

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PDF.pdf

and look at this link for other stuff

http://madasmaths.com/archive_maths_...ed_topics.html
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cooldudeman
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(Original post by TeeEm)
PDF.pdf

and look at this link for other stuff

http://madasmaths.com/archive_maths_...ed_topics.html
Thanks.

Have you got questions like these? Where finding the limits are tricky.

In this one I still can't make sense out of it. Its just that z is between r and sqrt (1-r^2) which is so tricky for me.

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TeeEm
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(Original post by cooldudeman)
Thanks.

Have you got questions like these? Where finding the limits are tricky.

In this one I still can't make sense out of it. Its just that z is between r and sqrt (1-r^2) which is so tricky for me.

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look at
the multivariable integration files
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cooldudeman
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(Original post by TeeEm)
look at
the multivariable integration files
Remember when you told me about symmetry calculations in integrals that have no contribution. You said if there's any odd powers of x or y then it has no contribution. Is this technique only for double integrals?

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TeeEm
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(Original post by cooldudeman)
Remember when you told me about symmetry calculations in integrals that have no contribution. You said if there's any odd powers of x or y then it has no contribution. Is this technique only for double integrals?

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any odd function integrated in a symmetrical domain equals zero.

it applies to any integral, single, double triple, parametric, vector, surface etc.


trig functions integrated over certain ranges have no contribution either but this is harder to explain ...
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cooldudeman
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(Original post by TeeEm)
any odd function integrated in a symmetrical domain equals zero.

it applies to any integral, single, double triple, parametric, vector, surface etc.


trig functions integrated over certain ranges have no contribution either but this is harder to explain ...
I have learned about odd and even functions and and if it is odd then on a symmertrical domain, the integral would be zero.

And we were told that sinx is odd. That means sin(f(x)) is also odd right? Where f id any function.

Also how does this hold here. We have x which when integrated is zero but how would you know if x is an odd function?

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TeeEm
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(Original post by cooldudeman)
I have learned about odd and even functions and and if it is odd then on a symmertrical domain, the integral would be zero.

And we were told that sinx is odd. That means sin(f(x)) is also odd right? Where f id any function.

Also how does this hold here. We have x which when integrated is zero but how would you know if x is an odd function?

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I am not sure what exactly you are asking me.

what holds where?
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cooldudeman
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(Original post by TeeEm)
I am not sure what exactly you are asking me.

what holds where?
Never mind I just figured it out.

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TeeEm
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(Original post by cooldudeman)
Never mind I just figured it out.

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here are 2 questions with a lot of simplifications due to "symmetries"


the first has Cartesian simplifications
VI.pdf


the second one has trigonometric simplifications.
BIT.pdf


See if they help
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cooldudeman
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(Original post by TeeEm)
I am not sure what exactly you are asking me.

what holds where?
When we normally parametrise we almost always give the range of theta for eq as 0 to 2pi. Can we purposely put something like -pi to pi so we can consider symmerty cancellations?

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TeeEm
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(Original post by cooldudeman)
When we normally parametrise we almost always give the range of theta for eq as 0 to 2pi. Can we purposely put something like -pi to pi so we can consider symmerty cancellations?

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sometimes is possible.
but if you have trig functions there more symmetries so you may not need that.
Graph knowledge very important too


e.g.

sinx, cosx, sin3x, cos5x, sin7x, sinxcosx, sinxcos2x, cosxsin4x etc yield zero from 0 to 2pi

others do not need a full range 0 to 2pi

cosx, sin2x, cos4x etc yields zero from 0 to pi


I also use gamma and beta functions so use more results
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cooldudeman
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(Original post by TeeEm)
sometimes is possible.
but if you have trig functions there more symmetries so you may not need that.
Graph knowledge very important too


e.g.

sinx, cosx, sin3x, cos5x, sin7x, sinxcosx, sinxcos2x, cosxsin4x etc yield zero from 0 to 2pi

others do not need a full range 0 to 2pi

cosx, sin2x, cos4x etc yields zero from 0 to pi


I also use gamma and beta functions so use more results
That seems like every trig function lol.

So this is not the case for ones like (sinx)^2 right? Because that is what usually what I have to integrate in our questions.
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