Which integral represents the limit as x approaches inf. of 1/n(√(1/n) + √(2/n) + ... √(n/n))?

Question

A. int from 0 to 1 of x dx
B. int from 0 to 1 of √x dx
C. 1/2 * int from 0 to 1 of 1/√x dx
D. 2 * int from 1 to 2 of x√x dx

Answer 1

recall that the Riemann sum is

sum f(xi) ∆x
Here, ∆x = 1/n, so the interval has width 1

That means it's not D

xi = 0+√(1/n * i)

so, it looks like ∫[0,1] √x dx