Could someone please help me solve this question? and if you could explain how as well I would really appreciate it

Question

Approximate using three equal subintervals. Draw a picture of the graph of the function showing your rectangles. Indicate the width and height of each rectangle. Show clearly how you got your estimate.

Answer 1

Δx = width of each interval = (3-0) / 3 = 1

Let f(x) = 4x

Using right endpoints of the three intervals (1, 2, and 3),

Area of first rectangle = f(1)Δx, Area of second rectangle = f(2)Δx, Area of third rectangle = f(3)Δx

∫_{(0 to 3)} 4xdx ≈ f(1)Δx + f(2)Δx + f(3)Δx = 4 + 8 + 12 = 24