p=2acosx求其所围成的面积

p=2acosx
所求面积 = ∫(- π/2→π/2) (1/2)ρ^2 dθ,
= 2∫(0→π/2) (1/2)(2acosθ)^2 dθ
= 4a^2∫(0→π/2) (cosθ)^2 dθ
= 4a^2∫(0→π/2) (1 + cos2θ)/2 dθ
= 2a^2[θ + (1/2)sin2θ] |(0→π/2)
= 2a^2(π/2)
= πa^2