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anonymous
 one year ago
Medal** Please help
Interchange the order of the integration and evaluate the integral
anonymous
 one year ago
Medal** Please help Interchange the order of the integration and evaluate the integral

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{pi}\int\limits_{\pi}^{\pi} \frac{ siny }{ y }dydx\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Are those the right intervals?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Ok, think of it this way dw:1436942548336:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oki...how do i change my limits

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Well 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
 one year ago
Best ResponseYou've already chosen the best response.0ok so my limits flip?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Sec, I don't think it's continous

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3dw:1436943113232:dw this is how your graph would like right

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Ok, so now that should be easy to interchange, dw:1436943501108:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0only my second integral changes right?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Well, we should get \[\int\limits_{0}^{\pi} \int\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thought it would be from x to pi

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Notice how x is horizontal, also it wouldn't make sense when you are integrating to have x after right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right because its dy dx

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3I'm a bit skeptical about the graph mhm

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Maybe I'm just a bit tired haha, well does it look good to you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i understand what your doing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i would intregate siny/y from o to y first?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would i do quotient rule to intregrate?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3What do you mean?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Like derivatives?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah im a bit confused on how to integrate siny/y

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3No, remember we are integrating respect to x, so we treat siny/y as a constant

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3I'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

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3dw:1436944319331:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{\pi}^{\pi}f(x)\,dx = 0\] am i missing somthing here ?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yeah, exactly, but I wasn't really sure whether the interchange should make a difference or not

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1it shouldn't because we must get the same answer either way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0are the limits 0 to y. correct then?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3No the limits are wrong, I knew it...something seemed fishy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how to find them? drawing again?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be pi to x?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1The problem itself is messed up, please double check the limits in original question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i just checked again...those are th limits given in the practice test

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3\[\int\limits\limits_{0}^{\pi} \int\limits\limits_{x}^{\pi}\] my drawing is for this

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1as you can see the original integral, asitis, evaluates to 0. end of story. take a screenshot and attach if you want to further debug for a possible typo..

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yeah this problem is a bit weird lol

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1because both \(x\) and \(\pi\) look alike typographically

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Mine 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
 one year ago
Best ResponseYou've already chosen the best response.0hmm oki lets go with x...since pi to pi doesnt make sense

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yeah i think thats the best we can do

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yeah lets treat it like x, you'll learn this way to I guess

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3dw:1436944946903:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0alright so our new limits would be in respect to the drawing

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So go ahead and integrate what we originally had

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3\[\large \int\limits\limits_{0}^{\pi} \int\limits\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0siny/y changes to siny/y *y= siny?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got 1 for the first integration

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \int\limits_{0}^{\pi}\int\limits_{x}^{\pi} \frac{ \sin y }{ y }\,dydx = \int\limits_{0}^{\pi}\int\limits_{0}^{y} \frac{ \sin y }{ y }\,dxdy = \int\limits_0^{\pi} \frac{\sin y}{y}*y \,dy = 2\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3dw:1436945173549:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes thank you so much!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3and that should = 2 as ganeshie showed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Ahh right, my mistake, it should be +2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow thank you so much you guys!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Np, you can finish it off right to get 2?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yeah 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

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Alright cool, good luck on your exam :)
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