" (i) "sin^(-1)(3x-4x^(3))=3sin^(-1)x,|x|<=(1)/(2)

Prove the following: sin^(-1)(3x-4x^(3))=3sin^(-1)x, x epsilon[-1/2,1/2]

int(sin^(-1)(3x-4x^3)dx)

int sin^(-1)(3x-4x^(3)) dx =

Prove that sin^(-1)(3x-4x^3)=3sin^(-1)x,x in[1/2,1]

int Sin^(-1) (3x-4x^(3))dx=

int(sin^(-1)(3x-4x^(3))dx)

int sin^-1 (3x-4x^3)dx

Each question contains statement given in two columns. Statement a,b in column I have to be matched with statement p,q in column II Column I, Column II cos^(-1)(4x^3-3x)=3cos^(-1)x ,then x can take values , p. [1/2,1] sin^(-1)(3x-4x^3)=3sin^(-1)x ,then x can take values , q. [-1/2,0]

Statement I If y=sin^(-1)(3x-4x^(3)), then (dy)/(dx)=(3)/(sqrt(1-x^(2))) only when (-1)/(2)lexlt(1)/(2)/. Statement II sin^(-1)(3x-4x^(3)) ={(-pi-3sin^(-1)x,,-1lexle-(1)/(2),),(3sin^(-1)x,,-(1)/(2)lexle(1)/(2),),(pi-3sin^(-1)x,,(1)/(2)lexle1,):}