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Topic: definite integral
Replies: 2   Last Post: May 26, 2014 3:19 AM

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Christopher Creutzig

Posts: 269
Registered: 2/24/09
Re: definite integral
Posted: May 26, 2014 3:19 AM
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On 04.05.14 23:28, Roger Stafford wrote:
> "semiha" wrote in message <lk4s60$1aj$1@newscl01ah.mathworks.com>...
>> i have defined as a symbolic x and t
>> c=(abs([(1 - 4*(1 +2*i*t)/(1 +4 *( x)^2+4*(t^2)))]))^2
>> such a function i want to integrate this function which x from -300 to 300 and write
>> a= int(c,x,-300,300)
>> and ezplot(c,t)
>> but matlab doesn't calculate "a" and doesn't plot

> - - - - - - - - - -
> I am not sure what is causing your trouble. The integrand can be expressed as the equivalent expression without complex numbers:
>
> c = 16*(1+4*t^2)/(1+4*t^2+4*x^2)^2-8/(1+4*t^2+4*x^2)+1


Only if you assume t to be real. If you do that, MATLAB has no problem
with the integral, either:

>> syms x t real
>> c=(abs([(1 - 4*(1 +2*i*t)/(1 +4 *( x)^2+4*(t^2)))]))^2;
>> a = int(c,x,-300,300)


a =

4800/((4*t^2 + 1)*(4*t^2 + 360001)) + 64*t^2*(300/((4*t^2 + 1)*(4*t^2 +
360001)) + atan((300*(8*t^2 + 2))/(4*t^2 + 1)^(3/2))/(2*(4*t^2 +
1)^(3/2))) - (32*t^2*atan(600/(4*t^2 + 1)^(1/2)))/(4*t^2 + 1)^(3/2) + 600

>> a = simplify(a,'Steps',1000)

a =

4800/(4*t^2 + 360001) + 600


HTH,

Christopher




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