计算定积分∫(上限1下限-1) (2x^2+x^3*cosx)/(1+√(1-x^2))dx_数学解答

计算定积分∫(上限1下限-1) (2x^2+x^3*cosx)/(1+√(1-x^2))dx

人气：161 ℃　时间：2020-03-22 05:30:58

解答

∵x^3*cosx/(1+√(1-x^2))是奇函数∴∫[x^3*cosx/(1+√(1-x^2))]dx=0故∴∫[(2x^2+x^3*cosx)/(1+√(1-x^2))]dx=2∫[x^2/(1+√(1-x^2))]dx+∫[x^3*cosx/(1+√(1-x^2))]dx=2∫[x^2/(1+√(1-x^2))]dx=2∫[x^2(1-√(1-x^...