Estimate the area under the graph of f(x)=x2+3x from x=5 to x=8 using 3 approximating rectangles and left endpoints.

Answer 1

Divide the interval [5,8] into 3 equal sections each of length Δx = (8-5) / 3 = 1

The left endpoints of the three intervals are 5, 6, and 7

Also, f(x) is positive throughout the interval [5,8].

Area ≈ f(5)Δx + f(6)Δx + f(7)Δx = f(5) + f(6) + f(7) (since Δx = 1)

Plug in and evaluate.