Jean-Marc Gulliet
science forum beginner
Joined: 28 May 2005
Posts: 38
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 Posted: Sun May 21, 2006 2:20 pm Post subject:
Re: integral problem
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haibozh@gmail.com wrote:
| Quote: | Hi, everyone
I have trouble in solving an integral problem. I couldn't get an
exact answer. Could anyone give me a hand?
\int_{0}^{2\pi} (a-bcos(u))^{3/2} du where a and b are
both constant.
Thanks in advance!
W.li.
Here is what I get with Mathematica 5.2 for Windows. The first answer |
depends on the values of the complex coefficients a and b. The second
answer is restricted to a and b positive reals and a > b.
In[1]:=
Integrate[(a - b*Cos[u])^(3/2), {u, 0, 2*Pi}]
Out[1]=
If[Re[a] > Re[b] && Re[a + b] > 0 &&
a a a
(Re[-] >= 1 || Re[-] <= -1 || Im[-] != 0),
b b b
1 2 b
- (8 a Sqrt[a - b] EllipticE[-(-----)] +
3 a - b
2 b
8 a Sqrt[a + b] EllipticE[-----] -
a + b
2 b
2 (Sqrt[a - b] (a + b) EllipticK[-(-----)] +
a - b
2 b
(a - b) Sqrt[a + b] EllipticK[-----])),
a + b
3/2
Integrate[(a - b Cos[u]) , {u, 0, 2 Pi},
Assumptions ->
a a
(Im[-] == 0 && -1 < Re[-] < 1) ||
b b
Re[a] <= Re[b] || Re[a + b] <= 0]]
In[2]:=
Integrate[(a - b*Cos[u])^(3/2), {u, 0, 2*Pi}, Assumptions -> {a > b > 0}]
Out[2]=
1 2 b
- (8 a Sqrt[a - b] EllipticE[-(-----)] +
3 a - b
2 b
8 a Sqrt[a + b] EllipticE[-----] -
a + b
2 b
2 (Sqrt[a - b] (a + b) EllipticK[-(-----)] +
a - b
2 b
(a - b) Sqrt[a + b] EllipticK[-----]))
a + b
HTH,
Jean-Marc |
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