_ x 0 (1^ cosec ^2 x +2^ cosec ^2 x + +n^ cosec ^2 x )^ ^2 x is equal to

Step-by-step solution

Let y= cosec ^2 x , aligned & Required limit = _ y (y^y+2^y+ n^y )^ 1 / y & = _ y (n^y )^ 1 / y (0 / form ) & [ ( 1 n )^y+ ( 2 n )^y+ + ( n-1 n )^y+1 ]^ 1 / y & = _ y n [ ( 1 n )^y+ ( 2 n )^y+ + ( n-1 n )^y+1 ]^ 1 / y & =n 1^0=n 1=n aligned