a problem about integration
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I want to do an integral like the picture. In the end, "x" will remain in the result expression. Anybody can help me?
3 Comments
Roger Stafford
on 9 Dec 2014
Even though no explicit expression is possible for this integral which depends on x, it is quite possible for you to devise a matlab function which takes x as its input and gives as an output the value of your integral using either numerical integration or the power series I have given you. In turn this function can be used for creating or helping to create the integrand for an outer integral.
See http://www.mathworks.com/help/matlab/ref/integral.html for the requirements on integrand functions for the numerical quadrature function 'integral', including the necessity for them to accept vector inputs.
Accepted Answer
Roger Stafford
on 7 Dec 2014
Edited: Roger Stafford
on 7 Dec 2014
Just in case it is of interest to you, here is that infinite series expansion of your integral which I referred to:
-2*pi*((x/2)/(0!*1!) + (x/2)^3/(1!*2!) + (x/2)^5/(2!*3!) + ...
+ (x/2)^(2*n-1)/((n-1)!*n!) + ... )
It is obtained using the Taylor Series expansion of your function about x = 0 and using the identity
int(cos(t)^n,'t',0,pi/2) = (1*3*5*...*(n-1))/(2*4*6*...*n)*pi/2
where n is an even integer.
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