Question

question 8
does the right riemann sum underestimate or overestimate the area of the region under the graph of a positive
increasing function? explain.
no correct answer choice is given.
underestimates, the rectangles all fit under the curve.
overestimates, the rectangles all fit under the curve.
underestimates, the rectangles do not fit under the curve.
overestimates, the rectangles do not fit under the curve.

Explanation:

For a positive increasing function, when using the right Riemann sum, the height of each rectangle is determined by the function value at the right - hand endpoint of each sub - interval. Since the function is increasing, the function value at the right - hand endpoint of a sub - interval is greater than the function values at all other points within that sub - interval. So, the rectangles formed by the right Riemann sum will have areas that are larger than the area of the region under the curve within each sub - interval.

Answer:

Overestimates, the rectangles do not fit under the curve.