Medal** Please help
Interchange the order of the integration and evaluate the integral

- anonymous

Medal** Please help
Interchange the order of the integration and evaluate the integral

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- anonymous

\[\int\limits_{0}^{pi}\int\limits_{\pi}^{\pi} \frac{ siny }{ y }dydx\]

- Astrophysics

Are those the right intervals?

- anonymous

yes

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## More answers

- Astrophysics

Ok, think of it this way |dw:1436942548336:dw|

- anonymous

oki...how do i change my limits

- Astrophysics

Well we have to draw it out, but as it's continuous we can say \[\int\limits_{a}^{b} \int\limits_{c}^{d} f(x,y) dy dx = \int\limits_{c}^{d} \int\limits_{a}^{b} f(x,y) dxdy\]

- anonymous

ok so my limits flip?

- Astrophysics

Sec, I don't think it's continous

- Astrophysics

|dw:1436943113232:dw| this is how your graph would like right

- anonymous

yes it would

- Astrophysics

Ok, so now that should be easy to interchange, |dw:1436943501108:dw|

- anonymous

only my second integral changes right?

- Astrophysics

Well, we should get \[\int\limits_{0}^{\pi} \int\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]

- anonymous

why isnt it o to x?

- anonymous

i thought it would be from x to pi

- Astrophysics

Notice how x is horizontal, also it wouldn't make sense when you are integrating to have x after right?

- anonymous

right because its dy dx

- Astrophysics

I'm a bit skeptical about the graph mhm

- Astrophysics

Maybe I'm just a bit tired haha, well does it look good to you?

- anonymous

i understand what your doing

- anonymous

i would intregate siny/y from o to y first?

- Astrophysics

Yup

- anonymous

would i do quotient rule to intregrate?

- Astrophysics

What do you mean?

- Astrophysics

Like derivatives?

- anonymous

yeah im a bit confused on how to integrate siny/y

- Astrophysics

No, remember we are integrating respect to x, so we treat siny/y as a constant

- Astrophysics

I'm still skeptical about the graph, it's throwing me off, and I'm a bit tired to confirm I'm going to tag the illustrious @ganeshie8 to confirm

- anonymous

ok thank you...

- Astrophysics

|dw:1436944319331:dw|

- ganeshie8

\[\int\limits_{\pi}^{\pi}f(x)\,dx = 0\]
am i missing somthing here ?

- Astrophysics

Yeah, exactly, but I wasn't really sure whether the interchange should make a difference or not

- ganeshie8

it shouldn't because we must get the same answer either way

- anonymous

are the limits 0 to y. correct then?

- Astrophysics

No the limits are wrong, I knew it...something seemed fishy

- anonymous

how to find them? drawing again?

- anonymous

would it be pi to x?

- ganeshie8

The problem itself is messed up, please double check the limits in original question

- anonymous

i just checked again...those are th limits given in the practice test

- Astrophysics

\[\int\limits\limits_{0}^{\pi} \int\limits\limits_{x}^{\pi}\] my drawing is for this

- ganeshie8

as you can see the original integral, as-it-is, evaluates to 0. end of story.
take a screenshot and attach if you want to further debug for a possible typo..

- Astrophysics

Yeah this problem is a bit weird lol

- anonymous

##### 1 Attachment

- ganeshie8

because both \(x\) and \(\pi\) look alike typographically

- anonymous

the first question

- Astrophysics

Mine works if you have an x, I'm going to stick with it being x haha, the other does not make sense, now I think that is an x instead of pi.

- anonymous

hmm oki lets go with x...since pi to pi doesnt make sense

- ganeshie8

yeah i think thats the best we can do

- Astrophysics

Yeah lets treat it like x, you'll learn this way to I guess

- Astrophysics

|dw:1436944946903:dw|

- anonymous

alright so our new limits would be in respect to the drawing

- Astrophysics

So go ahead and integrate what we originally had

- Astrophysics

\[\large \int\limits\limits_{0}^{\pi} \int\limits\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]

- anonymous

siny/y changes to siny/y *y= siny?

- Astrophysics

Mhm?

- anonymous

i got 1 for the first integration

- ganeshie8

\[\large \int\limits_{0}^{\pi}\int\limits_{x}^{\pi} \frac{ \sin y }{ y }\,dydx = \int\limits_{0}^{\pi}\int\limits_{0}^{y} \frac{ \sin y }{ y }\,dxdy = \int\limits_0^{\pi} \frac{\sin y}{y}*y \,dy = -2\]

- anonymous

not just 2?

- Astrophysics

|dw:1436945173549:dw|

- Astrophysics

Make sense?

- anonymous

yes thank you so much!

- Astrophysics

and that should = 2 as ganeshie showed

- ganeshie8

Ahh right, my mistake, it should be +2

- Astrophysics

Yeah haha

- anonymous

wow thank you so much you guys!

- Astrophysics

Np, you can finish it off right to get 2?

- anonymous

yes :)

- Astrophysics

Ok cool

- Astrophysics

Yeah about earlier, the question wasn't really making sense to me, because when we have such integrals \[\int\limits_{x}^{x} dx = 0\] it makes sense right using FTC

- anonymous

yes i agree

- Astrophysics

Alright cool, good luck on your exam :)

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