Question

高数积分题，求大神解答，谢谢

高数积分题，求大神解答，谢谢如图

Answer 1

如图所示：

追答

楼上的凑微分错得离谱

Answer 2

F'(x) = arcsin(x-1)^2, F(0) =0 ???     

是不是 F(1) =0

∫arcsinx dx

=xarcsinx -  ∫x/√(1-x^2 )  dx

=xarcsinx +(1/2)  ∫d(1-x^2)/√(1-x^2 )

=xarcsinx +√(1-x^2 ) + C

/

∫(0->1) F(x) dx

=[xF(x)]|(0->1) -∫(0->1) xF'(x) dx

=F(1) -∫(0->1) xarcsin(x-1)^2 dx

=0 -(1/2)∫(0->1) arcsin(x-1)^2 d(x-1)^2

=-(1/2)[ (x-1)arcsin(x-1) +√{1-(x-1)^2 } ]|(0->1)

=-(1/2) [ ( 0+1) -(π/2+ 0) ]

=π/4 - 1/2