Second moments of area/inertia for complex shapes

Hello,

I am working on my dissertation for aerospace engineering. I am designing a pitch control system to reduce vibration loads in wind turbine structures.

I am currently trying to produce a mathematical model to represent the bending of the wind turbine blades, and I have got stuck because I do not know how to find the second moments of inertia of the aerofoil cross section.

I know how to find Ix and Iy for simple shapes, but I am sure there must be a way to, for example, find the moments of inertia for a line defined by a polynomial equation.

I do have an idea, but I dont trust my judgement so if anyone could check it or suggest another method I would be really grateful.

HERE IS MY IDEA:

I know that Ix=int(y^2)dA, and since the blade cross-section is hollow I can define the area as the skin thickness (t) multiplied by the incremental distance which is tangent to the skin (ds) The aerofoil cros section shape is defoned by a polynomial equation y=f(x). If i can express y and ds in terms of x, I think I can solve the integral and find Ix.

Do any of you guys know if this is accurate?

Thanks, Adam