AP EAMCET2014MathematicsIndefinite Integration
For any integer n 2 , let I_n= ^n x d x . If I_n= 1 a ^ n-1 x-b I_ n-2 for n 2 , then the ordered pair (a, b) equals to
Options
- A(n-1, n-1 n-2 )
- B(n-1, n-2 n-1 )
- C(n, 1)
- D(n-1,1)
Correct answer
D. (n-1,1)
Step-by-step solution
Given, I_n= ^n x d x aligned & = ^ n-2 x ^2 x d x & = ^ n-2 ( ^2 x-1 ) d x & = ^ n-2 ^2 x d x- ^ n-2 d x & = ^ n-1 n-1 -I_ n-2 & [ array l put tan x=t ^2 x d x=d t . ^ n-2 d t= t^ n-1 n-1 = x^ n-1 n-1 ] array ] aligned But it is given aligned & I_n= 1 a ^ n-1 -b I_ n-2 & 1 a = 1 n-1 and b=1 & a=n-1, b=1 & (a, b)=(n-1,1) aligned