Limit

By observation, h = (2 - 1)/n, so a = 1, b = 2

And f(a + kh) = f(1 + k/n) = sqrt(1 + k/n)

So, f(x) = sqrt(1 + x)

On [1, 2], f(x) is positive and integrable (as sqrt(1 + x) > 0 for x in [1, 2] and is strictly increasing)

So, the limit becomes:

int (1→2) sqrt(1 + x) dx

= 2/3 [(1 + x)^(3/2)](1→2)

= 2/3 (3sqrt3 - 2sqrt2)

= 2sqrt3 - (4/3)sqrt2