Question

If the area under the curve of f(x) = x2 + 2 from x = 1 to x = 6 is estimated using five approximating rectangles and right endpoints, will the estimate be an underestimate or overestimate?

Underestimate
Overestimate
The area will be exact
The area cannot be estimated with just five rectangles

Answer 1

Overestimate

Explanation:

We draw five rectangles from x = 1 to x = 6, so each rectangle has a width of 1:

(6 - 1) / 5 = 1

We're using right endpoints to determine the height of each rectangle. The first rectangle is from x=1 to x=2, so the height of the rectangle is f(2) = 6. So on and so forth for the other rectangles.

The result is this:

desmos.com/calculator/vrl67vpigt

As we can see, these rectangles have areas outside of the curve, so their total area will be greater than the area under the curve. So this will be an overestimate.