experimentX
  • experimentX
find the shortest method to evaluate this \[ \int \frac{\sin x}{\sin x + \cos x} \; dx\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1347566427407:dw|
experimentX
  • experimentX
yeah that it is.
anonymous
  • anonymous
Do you know anything shorter?

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More answers

experimentX
  • experimentX
nope ... haven't found any other.
experimentX
  • experimentX
just noted how similar these two integrals look like \[ \int \frac{\sin x}{\sin x + \cos x} \; dx \\ \int \frac{\cos x}{\sin x + \cos x} \; dx \]
anonymous
  • anonymous
Note one more way. Although the same really, |dw:1347566670806:dw|
anonymous
  • anonymous
2I=pi/2 :)
anonymous
  • anonymous
^^ No limits here.
experimentX
  • experimentX
well ... pretty clever manipulation on the last problem
anonymous
  • anonymous
lol i thought there are ;)
experimentX
  • experimentX
yeah ... that is also very nice problem. i wish this one had too http://math.stackexchange.com/questions/198083/integrate-sin3x-sin3x-cos3x/198122#198122
experimentX
  • experimentX
interesting technique ...
anonymous
  • anonymous
maybe it does. |dw:1347567374847:dw|
experimentX
  • experimentX
there is one http://www.wolframalpha.com/input/?i=integrate%20%201/3%2bsin%28x%29/%283%28sin%28x%29%20%2b%20cos%28x%29%29%29%20-%202cos%282x%29/%283%2a%282%20-%20sin%282x%29%29%29 not nice and intuitive though
anonymous
  • anonymous
For 2, Taking six + cosx as t, |dw:1347567485586:dw|
experimentX
  • experimentX
this is just a back hack
anonymous
  • anonymous
back hack?
experimentX
  • experimentX
find the answer first ... differentiate the answer to get the get the middle portion.
anonymous
  • anonymous
How do you find the answer first?
experimentX
  • experimentX
make it easy as much a possible ... that's how i approach most of the problems. i to honest ... i can't work without answer.
anonymous
  • anonymous
Okay. Back hack, eh. Hmmmm.
experimentX
  • experimentX
Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.
anonymous
  • anonymous
Agreed.
experimentX
  • experimentX
well ... good night!!
anonymous
  • anonymous
Yeah. Goodnight. I'll think about this and get back to you tommorow. :)
anonymous
  • anonymous
Hold onn. What about the current solution to that, It does work quite easily or not?
anonymous
  • anonymous
To the sin^3x/sin^3x + cos^3x
experimentX
  • experimentX
there isn't nice manipulation like sin(x)/sin(x)+cos(x) for this one.

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