# How can I compute numerical integration from a multivariate function ( f(t,C) ) where C'=[c_1,c_2,...,c_m] with respect to " t "

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Siavash Kardar Tehran on 16 Oct 2013
Commented: Yannick on 17 Oct 2013
I want to find the numerical integration from a multivariate function ( f(t,C) ) where C'=[c_1,c_2,...,c_m] with respect to " t ",
what command is the most accurate and efficient Matlab command for doing this?
for example this is my function:
f(t,c_1,c_2,c_3,c_4) =
(t^2 + 1)*((5040315906112595*t^(3/5)*(156*c_1 - 156*3^(1/2)*c_2 + 156*5^(1/2)*c_3 - 156*7^(1/2)*c_4 + 195*3^(1/2)*c_2*t - 585*5^(1/2)*c_3*t + 1170*7^(1/2)*c_4*t + 450*5^(1/2)*c_3*t^2 - 2250*7^(1/2)*c_4*t^2 + 1250*7^(1/2)*c_4*t^3))/702561541869797376 + 1)^2 + (sin(t)*(c_1 - (exp(t)*((5040315906112595*t^(3/5)*(156*c_1 - 156*3^(1/2)*c_2 + 156*5^(1/2)*c_3 - 156*7^(1/2)*c_4 + 195*3^(1/2)*c_2*t - 585*5^(1/2)*c_3*t + 1170*7^(1/2)*c_4*t + 450*5^(1/2)*c_3*t^2 - 2250*7^(1/2)*c_4*t^2 + 1250*7^(1/2)*c_4*t^3))/702561541869797376 + 1))/2 + 3^(1/2)*c_2*(2*t - 1) + 5^(1/2)*c_3*(6*t^2 - 6*t + 1) + 7^(1/2)*c_4*(20*t^3 - 30*t^2 + 12*t - 1))^2)/cos(t)^2
note that the command " int ( f,t,0,1 ) " didn't work and it's said: Warning Explicit integral could not be found.
I'll be very appreciate if you help me with this.
Best regards,
Siavash.

Yannick on 16 Oct 2013
Edited: Yannick on 16 Oct 2013
Hi - a few things:
• INT is a Symbolic Math Toolbox command, so it will try to do the integration symbolically. In this case, since the function is quite complicated, it's having a hard time doing so.
• Instead, you probably want to try INTEGRAL if you have a recent enough MATLAB version, or QUAD otherwise.
• To handle the extra parameters, check out this doc page: Parameterizing Functions
Hope this helps!