Explanation:
that means that the given limit is the same as the integral between a and b over f(x). because the integral over a function is the area below the function curve (the integral IS the limit of such a sum).
we notice the format of a corresponding Riemann sum :
lim (with n to infinity) sum i=1 to n ((b-a)/n × f(a + (b-a)×i/n)) = integral a to b (f(x)dx).
we see therefore that
(b-a)/n = 6/n
b - a = 6
f(a + (b-a)×i/n) = sqrt(6 + 6i/n)
so, a = 6
b - 6 = 6
b = 12
and f(x) is simply sqrt(x)
so,
f(x) = sqrt(x)
A = 6
B = 12