Integrate cos(sin(x))

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Roshdy

Joined: 23 Nov 2005
Posts: 452
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Location: Egypt

20 Dec 2005 21:37 cos(sinx)

can anyone give a result for this integration

∫cos(sin(θ)) dθ

unlimited or limited by any values may reduce any complexity
Roshdy

steve10

Joined: 26 Mar 2002
Posts: 177
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Location: Los Angeles (Chinese)

21 Dec 2005 5:50 integrate cos(cos x)

I highly doubt that there is a finite expression of that integral. It can be expressed by a series if certain integration limits are applied.

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tantoun2004

Joined: 23 Jan 2005
Posts: 45
Helped: 3

21 Dec 2005 12:41 integration sin(sin(x))

Hi,
If this integral has limits of 0 to pi it will be equal to pi*J(0,x) where J(0,x) is Bessel function of order zero.
Regards,

venkateshr

Joined: 01 Feb 2005
Posts: 63
Helped: 2

28 Dec 2005 13:07 integrate cos(cos(x))

cos(sinx)= cos(cos(90-x))=cos^2(90-x)

i.e ∫cos²(90-x)dx which can be ∫ed easily right.

tantoun2004

Joined: 23 Jan 2005
Posts: 45
Helped: 3

28 Dec 2005 16:25 integral sin catalan

Hi,
This is not correct because cos(cos(90-x) is not equal to cos^(90-x) whis is equal to cos(90-x)*cos(90-x).
It can only be integrated numerically unless it has limits of 0 to pi where it's Bessel function..
Regards,

Roshdy

Joined: 23 Nov 2005
Posts: 452
Helped: 7
Location: Egypt

28 Dec 2005 20:46 cos integrates to sin

right
cos(cos(x)) doesn't equal to cos^2(x)
Roshdy

magnetra

Joined: 21 Apr 2005
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02 Oct 2009 18:58 Re: Integrate cos(sin(x))

What will be the integral
$3$ \frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta$

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_Eduardo_

Joined: 31 Aug 2009
Posts: 5
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Location: Argentina

02 Oct 2009 21:55 Re: Integrate cos(sin(x))

magnetra wrote:

What will be the integral
$3$ \frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta$

See previous messages.

$3$ \int_{0}^{\pi} \cos ( \sin \tau) \,\mathrm{d}\tau = \int_{0}^{\pi} \cos ( \cos \tau) \,\mathrm{d}\tau$

--> $3$\frac{1}{\pi} \int_{0}^{\pi} \cos ( \cos \tau) \,\mathrm{d}\tau = J_0(1) = 0.7651976865$