S=∫ydx
=∫ a(1-cosφ) d a(φ-sinφ)
=a²·∫ (1-cosφ)² d φ
=a²·∫ (1-2cosφ+cos²φ) d φ
=a²·∫ (1-2cosφ + (1+cos(2φ) )/2 ) d φ
=a²·∫ (3/2 - 2cosφ + (1/2)·cos(2φ) ) d φ
=a²· ((3/2)φ - 2sinφ + (1/4)·sin(2φ) |
=3πa²