# Changing order of integration Watch

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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Q7

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#2

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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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**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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firstly the region is the first two bounded regions of sinx, between x = 0 and x =2pi

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stupid question

firstly the region is the first two bounded regions of sinx, between x = 0 and x =2pi

**TeeEm**)stupid question

firstly the region is the first two bounded regions of sinx, between x = 0 and x =2pi

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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#4

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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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**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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#5

**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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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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#6

**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 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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#7

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#8

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I thought it can be done in 2, but it's too late for me to work through: to for the +ve chunk etc?

**atsruser**)I thought it can be done in 2, but it's too late for me to work through: to for the +ve chunk etc?

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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#9

**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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(Original post by

PDF.pdf

and look at this link for other stuff

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

**TeeEm**)PDF.pdf

and look at this link for other stuff

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

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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#11

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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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**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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the multivariable integration files

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#13

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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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**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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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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(Original post by

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 ...

**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 ...

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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#15

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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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**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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what holds where?

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#19

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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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**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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but if you have trig functions there more symmetries so you may not need that.

Graph knowledge very important too

e.g.

sinx, cosx, sin

^{3}x, cos

^{5}x, sin

^{7}x, sinxcosx, sinxcos

^{2}x, cosxsin

^{4}x 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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(Original post by

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, sin

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

**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, sin

^{3}x, cos^{5}x, sin^{7}x, sinxcosx, sinxcos^{2}x, cosxsin^{4}x etc yield zero from 0 to 2piothers 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

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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