Question Number 104339 by bemath last updated on 21/Jul/20

Examine ∫_0 ^3  ((2x)/((1−x^2 )^(2/3) )) dx

Commented bybemath last updated on 21/Jul/20

thank you both

Answered by Ar Brandon last updated on 21/Jul/20

∫_0 ^3  ((2x)/((1−x^2 )^(2/3) )) dx=−∫_0 ^3  ((−2x)/((1−x^2 )^(2/3) )) dx  =−∫_0 ^3 ((d(1−x^2 ))/((1−x^2 )^(2/3) ))=∫_(−8) ^1 u^(−2/3) du  =[3(u)^(1/3) ]_(−8) ^1 =3+6=9

Answered by bramlex last updated on 21/Jul/20

Answered by Dwaipayan Shikari last updated on 21/Jul/20

∫_0 ^3 ((2xdx)/((1−x^2 )^(2/3) ))=−∫_0 ^3 (dt/t^(2/3) )=−3[t^(1/3) ]_0 ^3 =−3[(1−x^2 )^(1/3) ]_0 ^3 =9