Question

The value of integral ∫\(_0^?\frac {cos⁡n\theta d\theta }{cos⁡\theta-cos∅}\)=π\(\frac {sin⁡ n∅}{sin ⁡∅}\) is valid for the limit 0 to_____

(a) π

(b) 2π

(c) –π

(d) nπ

This question was addressed to me in examination.

This key question is from The Symmetric Airfoil in portion Incompressible Flow over Airfoils of Aerodynamics

Answer 1

Right option is (a) π

The best I can explain: This is a standard integral which is used many times in the study of airfoils. This is used to solve the transformed fundamental equation in thin airfoil theory where the chord length is expressed as θ=0 to θ=π.