积分∫x^3*sqr(1-x^2)dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 22:14:43
积分∫x^3*sqr(1-x^2)dx积分∫x^3*sqr(1-x^2)dx积分∫x^3*sqr(1-x^2)dx∫x^3*sqr(1-x^2)dx=-1/2∫x²√(1-x²)d

积分∫x^3*sqr(1-x^2)dx
积分∫x^3*sqr(1-x^2)dx

积分∫x^3*sqr(1-x^2)dx
∫x^3*sqr(1-x^2)dx
=-1/2∫x²√(1-x²)d(1-x²)
=1/2∫[(1-x²)-1]√(1-x²)d(1-x²)
=1/2∫[(1-x²)^(3/2)-(1-x²)^(1/2)]d(1-x²)
=1/2[(2/5)(1-x²)^(5/2)-(2/3)(1-x²)^(3/2)]+C
=(1/5)(1-x²)^(5/2)-(1/3)(1-x²)^(3/2)+C,(C是积分常数).