KVPY2014MathematicsDefinite Integration
Let I_ n = ₀^ / 2 x^ n x d x , where n is a non negative integer Then _ n=2 ^ ( I_ n n ! + I_ n-2 (n-2) ! ) equal
Options
- Ae^ / 2 -1- 2
- Be^ / 2 -1
- Ce^ / 2 - 2
- De ^ / 2
Correct answer
A. e^ / 2 -1- 2
Step-by-step solution
array l Sol- I_ n = ₀^ / 2 x^ n x d x I_ n +n(n-1) I_ n-2 = ( 2 )^ n array Also _ n=2 ^ ( 1_ n n ! + I_ n-2 (n-2) ! )= _ n=2 ^ ( I_ n +(n-2) ! I_ n-2 n ! )= _ n=2 ^ ( ( / 2)^ n n ! )=e^ / 2 -1- 2