求图中定积分,详细过程步骤

如图
2024-12-30 16:37:15
推荐回答(2个)
回答1:

=2π*1/2∫r²e^(-r²)dr²
=-π∫r²de^(-r²)
=-πr²e^(-r²)+π∫e^(-r²)dr²
=-πe^(-r²)

回答2:

=2pi∫r^3e^(-r²)dr=pi∫r²e^(r²)dr²
=pi∫xe^(-x)dx=piΓ(2)=pi