Answer to Question #167331 in Calculus for sad

Question

A function f(x) is strictly decreasing on the interval [a,b].Would a Right Riemann Sum overestimate or underestimate the definite integral from a to b f(x)dx? Explain your answer!

Answer 1

 If the function is decreasing then the Right Riemann sums underestimates the definite integral from a to b f(x)dx

Because, If f is decreasing, then its minimum will always occur on the right side of each interval, and its maximum will always occur on the left side of each interval. So for decreasing functions, the left Riemann sum is always an overestimate and the right Riemann sum is always an underestimate