Questions: Let f be the function graphed below. If three subintervals of equal length are used, draw rectangles whose area represents a right Riemann sum approximation of ∫ from 1 to 5.5 of f(x) dx. Width of each subinterval: □ The shaded area above, representing a right Riemann sum, is an of the integral ∫ from 1 to 5.5 of f(x) dx because the function is on the interval 1<x<5.5.

Solution Steps

The interval is from 1 to 5.5, so the total length is 5.5 - 1 = 4.5. We're using 3 subintervals, so the width of each is 4.5 / 3 = 1.5.

The subintervals are: [1, 2.5], [2.5, 4], [4, 5.5] The right endpoints are 2.5, 4, and 5.5.

Draw rectangles with the right endpoints determining the height and the calculated width (1.5). The first rectangle goes from x = 1 to x = 2.5, with height f(2.5). The second rectangle spans from x = 2.5 to x = 4, with a height of f(4). The last rectangle extends from x = 4 to x = 5.5, and its height is given by f(5.5).

Since the function is increasing on the interval (1, 5.5), the right Riemann sum will be an overestimate.

Final Answer