Question

用分部积分法计算下列定积分1、∫0→1 xe^-x dx 2、∫(0→1/2) arcsin xdx 要整个过程,

Answer 1

∫0→1 xe^-x dx =-∫(0,1)xde^(-x)=-[xe^(-x)(0,1)-∫(0,1)e^(-x)]

=-[e+e^x(0,1)]=1-2e

∫(0→1/2) arcsin xdx =xarcsinx(0,1/2)-∫(0→1/2)x/√(1-x^2)dx

=(1/2)(π/6)+[√(1-x^2)](0,(1/2)=π/12+(√3/2)-1