Find the limit of the Reimann sum

Question

the following sum 

√(36-(6/n))²•6/n +√(36-(12/n))²•6/n+^….+√36-(6n/n))²•6/n   is a right Riemann sum for the definite integral f(x)dx with upper bound 6 and lower bound 0

 

what is f(x) and what is the limit of these Reimann sums are n approaches infinity?

 

Answer 1

f(x) = 36 - x; lim R_n n →∞ = ∫₀⁶(36 - x)dx = (36x - x²/2)₀⁶ = 648