KCET2013MathematicsIndefinite Integration
^ n-1 x ^ n+1 x d x( where, n 0) is equal to
Options
- A^ n x n +C
- B- ^ n-1 x n-1 +C
- C- ^ n x n +C
- D^ n-1 x n-1 +C
Correct answer
C. - ^ n x n +C
Step-by-step solution
Let aligned I &= ^ n-1 x ^ n+1 x d x, (n 0) &= ^ n-1 x ^ n+1 x ² x ² x d x &= ^ n-1 x ^ n-1 x cosec ² x d x &= ^ n-1 x cosec ² x d x aligned Let t= x d t=- cosec ² x d x= t^ n-1 (-d t)=- ( t^ n n )+C=- 1 n ^ n x+C ( t= x)