题目

计算定积分∫上0下负1[(3x^4+3x^2+1)/(x^2+1)](ey)

提问时间：2021-03-17

答案

∫[-1,0](3x^4+3x²+1)/(x²+1) dx
=∫[-1,0] [3x²+1/(x²+1)] dx
=3∫[-1,0]x²dx+∫[-1,0][1/(1+x²)]dx
=3(x³/3)[-1,0]+(arctanx)[-1,0]
=1+arcntan(0)-arctan(-1)
=1-(-π/4)
=1+π/4
≈1.785398163