S=∫{θ=0~π/4}[2a^2cos2θ-a^2]dθ=a^2∫{θ=0~π/4}[2cos2θ-1]dθ=-πa^2/4+a^2∫{θ=0~π/4}cos2θd(2θ)
=-πa^2/4+a^2sin(2θ)|{0,π/4}=a^2-πa^2/4=(4-π)a^2/4；