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Science Forum Index » Mathematics Forum » Help needed with integral
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| Dono |
 Posted: Tue Apr 29, 2008 1:56 pm |
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I input the following into the web-based Mathematica and it timed out
before giving an answer. Can anyone help finding out if there is a
symbolic answer:
sin[x]*sqrt(1-a*(cos[x])^2*((1+sin[x])^2/(1+a*sin[x])^2+(1-
a)*cos[x]^2))
Please copy and paste the formula in order to avoid introducing
errors. Thank you. |
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| Dono |
| Posted: Tue Apr 29, 2008 2:02 pm |
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Sorry, wrong integrand, here is the correct one:
sin[x]*sqrt(1-a*(cos[x])^2((1+sin[x])^2/(1+a*(sin[x])^2)+(1-
a)*(cos[x])^2)) |
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| Eric Gisse |
| Posted: Tue Apr 29, 2008 3:21 pm |
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| Dono |
| Posted: Tue Apr 29, 2008 4:17 pm |
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On Apr 29, 6:22 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
Quote: Mathematica uses Sin[] and Cos[].
Tom Roberts
Dono wrote:
I input the following into the web-based Mathematica and it timed out
before giving an answer. Can anyone help finding out if there is a
symbolic answer:
sin[x]*sqrt(1-a*(cos[x])^2*((1+sin[x])^2/(1+a*sin[x])^2+(1-
a)*cos[x]^2))
Please copy and paste the formula in order to avoid introducing
errors. Thank you.
It recognized the lower case, this is not the problem. |
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| Dono |
| Posted: Tue Apr 29, 2008 4:18 pm |
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On Apr 29, 6:21 pm, Eric Gisse <jowr...@gmail.com> wrote:
Excellent! Thank you , Eric! |
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| Dono |
| Posted: Tue Apr 29, 2008 6:54 pm |
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On Apr 29, 9:42 pm, David W. Cantrell <DWCantr...@sigmaxi.net> wrote:
Quote: Dono <sa...@comcast.net> wrote:
On Apr 29, 6:21 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Apr 29, 4:02 pm, Dono <sa...@comcast.net> wrote:
Sorry, wrong integrand, here is the correct one:
sin[x]*sqrt(1-a*(cos[x])^2((1+sin[x])^2/(1+a*(sin[x])^2)+(1-
a)*(cos[x])^2))
http://img291.imageshack.us/img291/8664/integralvi2.jpg
Excellent! Thank you , Eric!
Your jubilation is, I think, premature. If you differentiate the supposed
antiderivative shown there, you get just
sin(x) sqrt(1 - a cos(x)^2)
which is not equal to the given integrand.
David
Hmm,
So, what is the correct answer? |
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| Eric Gisse |
| Posted: Tue Apr 29, 2008 7:38 pm |
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On Apr 29, 8:42 pm, David W. Cantrell <DWCantr...@sigmaxi.net> wrote:
Quote: Dono <sa...@comcast.net> wrote:
On Apr 29, 6:21 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Apr 29, 4:02 pm, Dono <sa...@comcast.net> wrote:
Sorry, wrong integrand, here is the correct one:
sin[x]*sqrt(1-a*(cos[x])^2((1+sin[x])^2/(1+a*(sin[x])^2)+(1-
a)*(cos[x])^2))
http://img291.imageshack.us/img291/8664/integralvi2.jpg
Excellent! Thank you , Eric!
Your jubilation is, I think, premature. If you differentiate the supposed
antiderivative shown there, you get just
sin(x) sqrt(1 - a cos(x)^2)
which is not equal to the given integrand.
Yes, it is. If you have Maple, Mathematica, or MATLAB, have one of
them [preferably Maple] apply the relevant simplify command to the
expression.
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| Tom Roberts |
| Posted: Tue Apr 29, 2008 8:22 pm |
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Mathematica uses Sin[] and Cos[].
Tom Roberts
Dono wrote:
Quote: I input the following into the web-based Mathematica and it timed out
before giving an answer. Can anyone help finding out if there is a
symbolic answer:
sin[x]*sqrt(1-a*(cos[x])^2*((1+sin[x])^2/(1+a*sin[x])^2+(1-
a)*cos[x]^2))
Please copy and paste the formula in order to avoid introducing
errors. Thank you.
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| David W. Cantrell |
| Posted: Tue Apr 29, 2008 11:42 pm |
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Dono <sa_ge@comcast.net> wrote:
Quote: On Apr 29, 6:21 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Apr 29, 4:02 pm, Dono <sa...@comcast.net> wrote:
Sorry, wrong integrand, here is the correct one:
sin[x]*sqrt(1-a*(cos[x])^2((1+sin[x])^2/(1+a*(sin[x])^2)+(1-
a)*(cos[x])^2))
http://img291.imageshack.us/img291/8664/integralvi2.jpg
Excellent! Thank you , Eric!
Your jubilation is, I think, premature. If you differentiate the supposed
antiderivative shown there, you get just
sin(x) sqrt(1 - a cos(x)^2)
which is not equal to the given integrand.
David |
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