>>111

cos(π/2) = cos(3*π/2) = 0

なので、少し面倒ですね。

∫_{0}^{2*π} 1 / (a^2 * cos^2(x) + b^2 * sin^2(x)) dx

=

∫_{-π/2}^{3*π/2} 1 / (b^2 * cos^2(x) + a^2 * sin^2(x)) dx

=

∫_{-π/2}^{π/2} 1 / (b^2 * cos^2(x) + a^2 * sin^2(x)) dx

+

∫_{π/2}^{3*π/2} 1 / (b^2 * cos^2(x) + a^2 * sin^2(x)) dx