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

来源:学生作业帮助网 编辑:作业帮 时间:2024/12/01 07:30:08
计算定积分∫上0下负1[(3x^4+3x^2+1)/(x^2+1)](ey)
x){nuӟ|m:V?edG- 5+LHԴI*'_~ vUGԩYC )`նp *cJj)ph&Cmf,\$ck}cMBmĢļ (P(0ԅ(5ԄJjo7qAg;; -L-- ͌m @

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

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