By the definition of the definite integral, the value of _ n ( 1^4 1^5+n^5 + 2^4 2^5+n^5 + 3^4 3^5+n^5 + + n^4 n^5+n^5 ) is

Step-by-step solution

aligned & array l _ n ( 1^4 1^5+n^5 + 2^4 2^5+n^5 + 3^4 3^5+n^5 + + n^4 n^5+n^5 ) _ r=0 ^ r=n r^4 r^5+n^5 = ₀^1 x^4 1+x^5 d x Put 1+x^5=t 5 x^4 d x=d t = ₁^2 1 5 t d t= 1 5 [ t]₁^2 = 1 5 [ 2- 1]= 2 5 array aligned