AP EAMCET20227 Jul 2022Morning ShiftMathematicsIndefinite IntegrationActual
k N, 1-k ^2 x ^k x ^2 x d x=
Options
- Ax ^ k+x +C
- Bx ^k x +C
- C^k x ^2 x+C
- Dk ^ k-1 x x+C
Correct answer
B. x ^k x +C
Step-by-step solution
I= 1-k ^2 x ^k x ^2 x d x aligned & = ( ^2 x-k ) ^k x d x & = ( x)^ -k ^2 x d x-k d x ^k x & =( x)^ -k ^2 x d x- aligned [(-k)( x)^ -k-1 x ^2 x d x ] d x-k d x ^k x aligned =( x)^ -k x+ & k ( x)^ -k & x x d x-k d x ^k x aligned = x ^k x +k d x ^k x -k d x ^k x +C= x ^k x +C