Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Integrate cos(sin(x))

Status
Not open for further replies.

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
 

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.
 

    Roshdy

    Points: 2
    Helpful Answer Positive Rating
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,
 

    Roshdy

    Points: 2
    Helpful Answer Positive Rating
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.
 

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,
 

cos integrates to sin

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

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


M
 
Last edited by a moderator:

magnetra said:
What will be the integral
\[ \frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta \]

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:

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top