MATLAB: Explicit integral could not be found problem

integration

Hello all,
I want to solve for definite integral. It is little complicated. I was unable to write it over here that is why I have attached pdf file along with this. It just contains 3 equations.
The matlab code for this is as follows:
clear all;
pd=0.015; dr=0.0614;
phi1=acosd(pd/(2*dr));
epsi=0.5*(1-pd/(2*dr));
syms theta;
f=(1/(2*pi))*(1-(0.5/epsi)*(1-cos(theta)))^(1.5)*cos(theta);
answer=int(f,theta,-phi1,phi1);
When I run the code I am getting following output:
Warning: Explicit integral could not be found. 
>> answer
answer =
int((5734161139222659*cos(theta)*((614*cos(theta))/539 - 75/539)^(3/2))/36028797018963968, theta = -5839466350469371/70368744177664..5839466350469371/70368744177664)
I have no clue how to debug this. Can somebody please help me how to solve this integral problem using MATLAB. For integral please refer to pdf file.
Thanks in advance
Nikhil

Best Answer

syms theta
pd = 15/1000;       %symbolics are easier to get right when rationals are used
dr = 614/10000;
epsilon = 1/2*(1-pd/(2*dr));
theta1 = acos(pd/(2*dr));
T = (1-(1-cos(theta))/(2*epsilon))^(3/2)*cos(theta);
f = simplify( 1/(2*pi) * int(T, theta, -theta1, theta1) );
Using Maple, the result I get is
 (1/127414210)*(2273226*3377^(1/2)*elliptice((2/77)*sin((1/2)*acos(75/614))*3377^(1/2), (7/614)*3377^(1/2))-1320813*3377^(1/2)*ellipticf((2/77)*sin((1/2)*acos(75/614))*3377^(1/2), (7/614)*3377^(1/2))+(1228*sin((3/2)*acos(75/614))-1828*sin((1/2)*acos(75/614)))*(617562121+636557746*cos(2*acos(75/614)))^(1/2)+2273226*(-(440271/757742)*elliptick((7/614)*3377^(1/2))+elliptice((7/614)*3377^(1/2)))*3377^(1/2))/pi
Which is approximately
0.218945210999261
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