Numerically integrating with weight factors

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Tyler 2013-8-17

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https://ww2.mathworks.cn/matlabcentral/answers/84984-numerically-integrating-with-weight-factors

Hi, i am integrating a stiffness matrix over two euler angles, phi, theta.

if i integrate the stiffness matrix over both angles, and then divide by the area of a unit sphere, it is treated as if each particular direction is weighted equally, and for a transversely isotropic material, when integrated will produce an isotropic material.

I am interested in biasing the integral however with a separate probability distribution (which i have at the moment as a gaussian curve revolved around an axis, in meshgrid form).

How do i specify when integrating - that i want the particular numerical integration function (say quad) to while integrating at a particular point phi,theta - to go and grab the weight factor from my table?

Is there any way to do this?

any help would be greatly appreciated.