1 - Calculus

Question

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counter example.

(a) True or False: The n-rectangle lower sum for f on [a, b] is always equal to the corresponding right sum. 

Step-by-Step Solution

Answer

The given statement is False

Step 1: Given Information

The $n-$Rectangle lower sum for $f$ on $[a, b]$ is always equal to the corresponding right sum.

Step 2: Calculation

The statement is,
The $n-$Rectangle lower sum for $f$ on $[a, b]$is always equal to the corresponding right sum.
The statement is false.
The upper sum is always greater than or equal to the actual signed area where as the lower sum is always less than or equal to the actual signed area.
Therefore, the statement is false 

Step 3: Conclusion

Therefore, the given statement is false