walters
compute the following integral
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walters
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\[ \int\limits_{\pi}^{\pi}\frac{ 1}{ 1+e ^{sinx} }dx\]
cluo
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its from pi to pi?
walters
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oh from -pi to pi
walters
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i only have the finaly answer (pi) but i don'tknow did they it
cluo
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what level is this?
walters
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second
cluo
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second what?
walters
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ok maybe i don't understand u which level are u refering to?
cluo
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which grade?
walters
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advanced calculus
cluo
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past vector calculus?
walters
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i did pure calculus now is the second level of it (which is advanced calculus)
cluo
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have you done double and triple integrals? i only ask because i think i saw something similar a couple days ago.
walters
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i am not sure whether this is possible
The substitution of x=-y yields
|dw:1360491262699:dw|
NB:not sure
walters
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@phi pls help
hartnn
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do you know a standard integral...
\(\int \limits_a^b f(x)dx =\int \limits_a^b f(a+b-x)dx \)
hartnn
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*standard property.
walters
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no
hartnn
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ok, then do you want to use this (1 method) or continue with what u did (another method) of putting x=-y...
walters
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any method u know u can use it i'll try to catch up
hartnn
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ok, i'll tell u both, first using your substitution x=-y,
|dw:1360492675542:dw|
|dw:1360492681874:dw|
understood till here ?
walters
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ok this means i will have
|dw:1360492779070:dw|
@hartnn can u pls teach me/explain standard property
hartnn
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yes, you got it correct using your method, now the standard property...
let I = integral ..... -------->(1)
now using that property, first tell what is a+b-x =.... ?
walters
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pi-pi-x=-x
hartnn
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yes, so, because of that property,
|dw:1360493289196:dw|
add 1 and 2
what u get ?
walters
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|dw:1360493238315:dw|
walters
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from -pi to pi
hartnn
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umm...not actually....
|dw:1360493484296:dw|
|dw:1360493501827:dw|
s = sin x
hartnn
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|dw:1360493565788:dw|
hartnn
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got that ^ ?
walters
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wow i see now so tell me how wil i know that i must use standart property
hartnn
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thats trial and error, i first thought of substitution, then recalled different properties, then this property was found to be useful...wih enough practice, this procedure becomes easy and fast...
hartnn
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also you must know all the properties beforehand ...
walters
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ok thnx
hartnn
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welcome ^_^
walters
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@jacobian see this