Help me solve this integration equation

[max232]

Integration,

Hi ,

I seek with intergrer this

I = (sin ( ( A *cos(x) ) ) / cos(x) )^(2) * sin^3 (x) dx

dx(0 to pi )

without using matlab

Thank you

 

[rudane]

Re: Integration,

Is your second set of brackets around Acos(x) there for a reason? For example, would I word your question as this:

The integration of [Sin(Acosx) over cosx all squared] [multiplied by sinx cubed] [multiplied by dx] (from pi to 0)

 

[max232]

Re: Integration,

The integration of [Sin(Acosx) over cosx all squared] [multiplied by sinx cubed] [multiplied by dx]

(from o to pi)

 

[john77]

Re: Integration,

I have attached a partial solution to your problem. You should be able to complete it now.

 

[lkuzu]

Re: Integration,

use Maple, and find the solution as:


Maple input> integral:=Int((sin(A*cos(x))/cos(x))^2 * sin (x)^3,x=0..Pi);

Pi
/ 2 3
| sin(A cos(x)) sin(x)
integral := | ---------------------- dx
| 2
/ cos(x)
0

Maple input> int((sin(A*cos(x))/cos(x))^2 * sin (x)^3,x=0..Pi);


-3 A + 2 A cos(A)*cos(A) + cos(A) sin(A) + 2 Si(2 A) A*A
-----------------------------------------------------------------
A



if A=1, answer: -2+cos(2)+cos(1)*sin(1)+2*Si(2)


regards,
Lkuzu

 

[Captain]

Re: Integration,

This is the result from mathematica