定积分(-5到5)x^2sinx^3⼀x^4+2x^2+1 dx 利用函数奇偶性计算

2024-12-03 20:37:50
推荐回答(1个)
回答1:

若是 I = ∫ [x^2(sinx)^3/(x^4+2x^2+1)] dx,则 I = 0.
若是 I = ∫ {[x^2(sinx)^3/x^4]+2x^2+1} dx,
则 I = 0 + ∫ (2x^2+1)dx = 2∫ (2x^2+1)dx
= 2[2x^3/3+x] = 530/3