∫(x-2)^(2/3)dx=
(t=x-2; dt=dx)
=∫t^(2/3)dt=t^(2/3+1)/(2/3+1)=t^(5/3)/(5/3)=3t^(5/3)/5=3(x-2)^(5/3)/5=
(подстановка)
=3(a-2)^(5/3)/5-3(b-2)^(5/3)/5=0.6((a-2)^(5/3)-(b-2)^(5/3))
![\int\limits^a_b {\sqrt[3]{ (x-2)}^{2}} \, dx](/tpl/images/3995/7395/bde1f.png)
∫(x-2)^(2/3)dx=
(t=x-2; dt=dx)
=∫t^(2/3)dt=t^(2/3+1)/(2/3+1)=t^(5/3)/(5/3)=3t^(5/3)/5=3(x-2)^(5/3)/5=
(подстановка)
=3(a-2)^(5/3)/5-3(b-2)^(5/3)/5=0.6((a-2)^(5/3)-(b-2)^(5/3))