Help on calculus please: Area approximation

Question

Write the summation to estimate the area under the curve  from x = 2 to x = 5 using 3 rectangles and right endpoints

Options:

1. 
2. 
3. 
4. 

Answer 1

Let f(x) = 2 + √x and Δx = (5-2)/3 = 1

Area ≈ f(3)Δx + f(4)Δx + f(5)Δx = (2+√3) + (2+√4) + (2+√5) = ∑_{(i = 3 to 5)} [2 + √i]

Answer: choice 4