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