∫ ^(1/4)_(0)dx/sqrt(1-(3x)^2)=
d(3x)=3dx ⇒ dx=(1/3)d(3x)
=(1/3) ∫ ^(1/4)_(0)d(3x)/sqrt(1-(3x)^2)=
=(1/3)arcsin(3x)|^(1/4)_(0)=
=(1/3)arcsin(3/4)-(1/3)arcsin0=
=(1/3)arcsin(3/4)-(1/3)*0=
= [b](1/3)arcsin(3/4)[/b]
2.
∫ ^(6)_(2)sqrt(x-2)dx= ∫ ^(6)_(2)(x-2)^(1/2)d(x-2)=
=(x-2)^(3/2)/(3/2)|^(6)_(2)=
=(2/3)(x-2)^(3/2)|^(6)_(2)=
=(2/3)(6-2)^(3/2)-(2/3)*(2-2)^(3/2)=
=(2/3)*4^(3/2)=(2/3)*sqrt(4^3)=(2/3)*sqrt(64)=(2/3)*8= [b]16/3[/b]