How do I integrate a Fractional Trigonometric function in Matlab?

Hi

I want to integrate

ki = k /((2*pi)^(alpha-1)*int(0-2*pi) cos(theta)^alpha*2^(beta-alpha)).

where k=1, alpha =1.35, beta = 2.09.

I have tried the following in matlab:

1.

fun1 = @(theta) (cos(theta)).^alpha*(2).^(beta-alpha);
q1 = integral(fun1,0,2*pi);
d1 = (2*pi)^(alpha-1);
ki = k/(d1*q1);

2.

int(((cos(x))^alpha*2^(beta-alpha),0, 2*pi)

But I am getting incorrect answers, i.e. they do not match with my hand calculations. Am I using the incorrect format in matlab. Or is anyone of this method correct and I might be going wrong with my hand calculations?

Is there something different to use for fractional trignometric integration matlab?

Any help would be appreciated.

Thanks

Sneha

[Torsten]

I don't see the abs() in your function definitions.

[Sneha Thakur]

Thanks Torsten for pointing out my mistake.

But I am still not getting the correct answer, assuming my hand calculations are true.

Am I correct when integrating cos(theta) from 0-2*pi,

solution is

= [abs(sin(theta))]^alpha, 0-2*pi

= [abs(sin(2*pi)-sin(0))]^alpha

=0

matlab: sin(2*pi)-sin(0)

ans =

-2.4493e-16

>> abs(ans)

ans =

   2.4493e-16

>> ans^1.35

ans =

   8.4179e-22

Thanks

Sneha

[Torsten]

Your hand-calculations are wrong:

integral((cos(x))^alpha)

is not equal to

(sin(x))^Alpha

Hint:

d/dx ((sin(x))^alpha) = alpha*(sin(x))^(alpha-1)*cos(x)

[Sneha Thakur]

Thank You Torsten.

It has solved my problem to an extent.

Thanks

Sneha

[Ahmed Essam]

I want to integrate the function attached in the picture please