Dec 20, 2005 #1 Roshdy Member level 3 Joined Nov 23, 2005 Messages 57 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,286 Location Egypt Activity points 1,738 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
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
Dec 21, 2005 #2 S steve10 Full Member level 3 Joined Mar 26, 2002 Messages 175 Helped 32 Reputation 64 Reaction score 0 Trophy points 1,296 Location Los Angeles (Chinese) Activity points 2,538 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.
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.
Dec 21, 2005 #3 T tantoun2004 Member level 1 Joined Jan 23, 2005 Messages 41 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,286 Activity points 455 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,
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,
Dec 28, 2005 #4 V venkateshr Member level 3 Joined Feb 1, 2005 Messages 63 Helped 3 Reputation 6 Reaction score 2 Trophy points 1,288 Activity points 503 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.
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.
Dec 28, 2005 #5 T tantoun2004 Member level 1 Joined Jan 23, 2005 Messages 41 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,286 Activity points 455 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,
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,
Dec 28, 2005 #6 Roshdy Member level 3 Joined Nov 23, 2005 Messages 57 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,286 Location Egypt Activity points 1,738 cos integrates to sin right cos(cos(x)) doesn't equal to cos^2(x) Roshdy
Oct 2, 2009 #7 M magnetra Full Member level 5 Joined Apr 21, 2005 Messages 263 Helped 10 Reputation 20 Reaction score 7 Trophy points 1,298 Location 27.45N, 85.20E KTM, NP Activity points 3,375 What will be the integral \[ \frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta \] M Last edited by a moderator: Aug 27, 2010
Oct 2, 2009 #8 _Eduardo_ Full Member level 5 Joined Aug 31, 2009 Messages 295 Helped 118 Reputation 238 Reaction score 103 Trophy points 1,323 Location Argentina Activity points 2,909 magnetra said: What will be the integral \[ \frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta \] Click to expand... See previous messages. \[ \int_{0}^{\pi} \cos ( \sin \tau) \,\mathrm{d}\tau = \int_{0}^{\pi} \cos ( \cos \tau) \,\mathrm{d}\tau\] --> \[\frac{1}{\pi} \int_{0}^{\pi} \cos ( \cos \tau) \,\mathrm{d}\tau = J_0(1) = 0.7651976865 \] Last edited by a moderator: Aug 27, 2010
magnetra said: What will be the integral \[ \frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta \] Click to expand... See previous messages. \[ \int_{0}^{\pi} \cos ( \sin \tau) \,\mathrm{d}\tau = \int_{0}^{\pi} \cos ( \cos \tau) \,\mathrm{d}\tau\] --> \[\frac{1}{\pi} \int_{0}^{\pi} \cos ( \cos \tau) \,\mathrm{d}\tau = J_0(1) = 0.7651976865 \]