The correct formula for the Fourier sine series appearing in

the-correct-formula-for-the-fourier-sine-series-appearing-in

The correct formula for the Fourier sine series appearing in the solution of thin airfoil theory is_____

A. An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

B. An=\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

C. An=\(\frac {2}{\pi }\int_0^{2\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

D. An=α-\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

I had been asked this question in my homework.

Query is from The Cambered Airfoil in section Incompressible Flow over Airfoils of Aerodynamics

The correct answer is A. An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅

The explanation is: From the general solution of thin airfoil theory we have An=\(\frac {2}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅ and A0=α-\(\frac {1}{\pi }\int_0^{\pi }\frac {dz}{dx}\) cos⁡n∅ d∅ where the limits are 0≤∅≤π.