anonymous
  • anonymous
Medal** Please help Interchange the order of the integration and evaluate the integral
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{0}^{pi}\int\limits_{\pi}^{\pi} \frac{ siny }{ y }dydx\]
Astrophysics
  • Astrophysics
Are those the right intervals?
anonymous
  • anonymous
yes

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Astrophysics
  • Astrophysics
Ok, think of it this way |dw:1436942548336:dw|
anonymous
  • anonymous
oki...how do i change my limits
Astrophysics
  • 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
  • anonymous
ok so my limits flip?
Astrophysics
  • Astrophysics
Sec, I don't think it's continous
Astrophysics
  • Astrophysics
|dw:1436943113232:dw| this is how your graph would like right
anonymous
  • anonymous
yes it would
Astrophysics
  • Astrophysics
Ok, so now that should be easy to interchange, |dw:1436943501108:dw|
anonymous
  • anonymous
only my second integral changes right?
Astrophysics
  • Astrophysics
Well, we should get \[\int\limits_{0}^{\pi} \int\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]
anonymous
  • anonymous
why isnt it o to x?
anonymous
  • anonymous
i thought it would be from x to pi
Astrophysics
  • Astrophysics
Notice how x is horizontal, also it wouldn't make sense when you are integrating to have x after right?
anonymous
  • anonymous
right because its dy dx
Astrophysics
  • Astrophysics
I'm a bit skeptical about the graph mhm
Astrophysics
  • Astrophysics
Maybe I'm just a bit tired haha, well does it look good to you?
anonymous
  • anonymous
i understand what your doing
anonymous
  • anonymous
i would intregate siny/y from o to y first?
Astrophysics
  • Astrophysics
Yup
anonymous
  • anonymous
would i do quotient rule to intregrate?
Astrophysics
  • Astrophysics
What do you mean?
Astrophysics
  • Astrophysics
Like derivatives?
anonymous
  • anonymous
yeah im a bit confused on how to integrate siny/y
Astrophysics
  • Astrophysics
No, remember we are integrating respect to x, so we treat siny/y as a constant
Astrophysics
  • 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
  • anonymous
ok thank you...
Astrophysics
  • Astrophysics
|dw:1436944319331:dw|
ganeshie8
  • ganeshie8
\[\int\limits_{\pi}^{\pi}f(x)\,dx = 0\] am i missing somthing here ?
Astrophysics
  • Astrophysics
Yeah, exactly, but I wasn't really sure whether the interchange should make a difference or not
ganeshie8
  • ganeshie8
it shouldn't because we must get the same answer either way
anonymous
  • anonymous
are the limits 0 to y. correct then?
Astrophysics
  • Astrophysics
No the limits are wrong, I knew it...something seemed fishy
anonymous
  • anonymous
how to find them? drawing again?
anonymous
  • anonymous
would it be pi to x?
ganeshie8
  • ganeshie8
The problem itself is messed up, please double check the limits in original question
anonymous
  • anonymous
i just checked again...those are th limits given in the practice test
Astrophysics
  • Astrophysics
\[\int\limits\limits_{0}^{\pi} \int\limits\limits_{x}^{\pi}\] my drawing is for this
ganeshie8
  • 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
  • Astrophysics
Yeah this problem is a bit weird lol
anonymous
  • anonymous
1 Attachment
ganeshie8
  • ganeshie8
because both \(x\) and \(\pi\) look alike typographically
anonymous
  • anonymous
the first question
Astrophysics
  • 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
  • anonymous
hmm oki lets go with x...since pi to pi doesnt make sense
ganeshie8
  • ganeshie8
yeah i think thats the best we can do
Astrophysics
  • Astrophysics
Yeah lets treat it like x, you'll learn this way to I guess
Astrophysics
  • Astrophysics
|dw:1436944946903:dw|
anonymous
  • anonymous
alright so our new limits would be in respect to the drawing
Astrophysics
  • Astrophysics
So go ahead and integrate what we originally had
Astrophysics
  • Astrophysics
\[\large \int\limits\limits_{0}^{\pi} \int\limits\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]
anonymous
  • anonymous
siny/y changes to siny/y *y= siny?
Astrophysics
  • Astrophysics
Mhm?
anonymous
  • anonymous
i got 1 for the first integration
ganeshie8
  • 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
  • anonymous
not just 2?
Astrophysics
  • Astrophysics
|dw:1436945173549:dw|
Astrophysics
  • Astrophysics
Make sense?
anonymous
  • anonymous
yes thank you so much!
Astrophysics
  • Astrophysics
and that should = 2 as ganeshie showed
ganeshie8
  • ganeshie8
Ahh right, my mistake, it should be +2
Astrophysics
  • Astrophysics
Yeah haha
anonymous
  • anonymous
wow thank you so much you guys!
Astrophysics
  • Astrophysics
Np, you can finish it off right to get 2?
anonymous
  • anonymous
yes :)
Astrophysics
  • Astrophysics
Ok cool
Astrophysics
  • 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
  • anonymous
yes i agree
Astrophysics
  • Astrophysics
Alright cool, good luck on your exam :)

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