If I= ₀^ x ^2( x)+ ^2( x) d x , then, [I]= . . Here,[.] denotes greatest integer function.

Step-by-step solution

We have, aligned & I= ₀^ x ^2( x)+ ^2( x) d x & I= ₀^ ( -x) [ ^2( ( -x)]+ ^2( ( -x)) d x . & I= ₀^ ( -x) [ ^2( x)+ ^2( x) ] d x aligned 2 I= ₀^ [ ^2( x)+ ^2( x) ] d x aligned & I= ₀^ / 2 [ ^2 ( ( 2 -x ) )+ ^2 ( ( 2 -x ) ) ] d x & I= ₀^ / 2 ^2( x)+ ^2( x) d x & 2 I= ₀^ / 2 2 d x I= ( 2 )= ^2 2 aligned [I]= [ ^2 2 ]=4 [ array l ^2 (9,10) ^2 2 (4.5,5) array ]