∫(1+x^3)cosx/1+sin^2 xdx 积分上限为π/2 下限为-π/2
问题描述:
∫(1+x^3)cosx/1+sin^2 xdx 积分上限为π/2 下限为-π/2
答
∫[-π/2,π/2 ](1+x^3)cosx/(1+sin^2 x)dx =∫[-π/2,π/2 ]cosx/(1+sin^2 x)dx +∫[-π/2,π/2 ]x^3cosx/(1+sin^2 x)dx (注意后面一项是奇函数,等于0)=∫[-π/2,π/2 ]cosx/(1+sin^2 x)dx=∫[-π/2,π/2 ]1/(1+s...