integral equation is in the pdf file
explicit integral could not be found problem
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Nikhil
am 29 Okt. 2013
Kommentiert: Nikhil
am 30 Okt. 2013
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
5 Kommentare
Walter Roberson
am 30 Okt. 2013
No you don't. You use phi1 as your bounds on the integral, where it becomes your theta variable, but you take cos() of theta not cosd(theta), so theta must be in radians so phi1 should be in radians.
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Walter Roberson
am 30 Okt. 2013
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
5 Kommentare
Walter Roberson
am 30 Okt. 2013
Nikhil, I do not have the Symbolic Toolbox, so I cannot report the exact form of the answer that MATLAB would give. Sometimes I am able to figure out the MuPAD commands from the documentation, but I cannot always predict the MuPAD output.
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