If I_ n = ₀^ / 4 ^ n x d x , where n is a positive integer, then I₁₀+I₈ is

Step-by-step solution

Given integral is, aligned I_ n &= ₀^ / 4 ^ n x d x I_ n &= ₀^ / 4 ^ n-2 x ² x d x &= ₀^ / 4 ^ n-2 x ( ² x-1 ) d x I_ n &= ₀^ / 4 ^ n-2 x ² x d x &- ₀^ / 4 ^ n-2 x d x aligned gathered I_ n = ₀¹ t^ n-2 d t- ₀^ / 4 ^ n-2 x d x I_ n = [ t^ n-1 n-1 ]₀¹-I_ n-2 array l put x=t ² x d x=d t array I_ n +I_ n-2 = 1 n-1 gathered Put n=10 , we get I₁₀+I₈= 1 9