AP EAMCET202018 Sep 2020Evening ShiftMathematicsDefinite IntegrationActual
If (I_n= ₀^ / 2 ^n(x) d x ) and (I_n=(k) I_ n-2 ), then what will be the value of (k ) ?
Options
- A( n n-1 )
- B( n-1 n )
- C( n+1 n )
- D( n n+1 )
Correct answer
B. ( n-1 n )
Step-by-step solution
( aligned I _n & = ₀^ / 2 x ^ n-1 x dx & .= ^ n-1 x(- x) ]₀^ / 2 + ₀^ / 2 (n-1) ^ n-2 x & =0+(n-1) ₀^ / 2 ^ n-2 x (1- ^2 x ) d x I _n & =(n-1) ₀^ / 2 ^ n-2 x d x-(n-1) ₀^ / 2 _x^n d x n I _n & =(n-1) I _ n-2 I _n & = n-1 n I _ n-2 aligned ) Hence, option (b) is correct.