∫(0，π/2)cos^nθdθ＝？

Answer 1

对于公式如∫(0→π/2) sinⁿ dx = ∫(0→π/2) cosⁿx dx,n > 1
当n是奇数时= (n - 1)!/n! = (n - 1)/n · (n - 3)/(n - 2) · (n - 5)/(n - 4) · ... · 3/4 · 1/2
当n是偶数时= (n - 1)!/n! · π/2 = (n - 1)/n · (n - 3)/(n - 2) · (n - 5)/(n - 4) · ... · 3/4 · 1/2 · π/2,多了个π/2

Answer 2