Question

Which of the following is/are true about Riemann Sums:

I. Typically, three methods are used: left sums, right sums and midpoint sums.
II. The more rectangles used, the closer the approximation is to the exact area under the curve.
III. The midpoint sums method is the average of the left sum and the right sum.
a. I and II
b. II and III
c. I
d. II

Answer 1

The correct answer is a. I and II. Riemann Sums can be approximated using three methods: left sums, right sums, and midpoint sums. The more rectangles that are used in the approximation, the closer it is to the exact area under the curve. The midpoint sums method does not involve averaging the left and right sums.

Step-by-step explanation:

The correct answer is a. I and II.

I. This statement is true. Riemann Sums can be approximated using three methods: left sums, right sums, and midpoint sums. These methods involve dividing the area under a curve into a series of rectangles and calculating the sum of the areas of those rectangles.

II. This statement is true. The more rectangles that are used in the Riemann Sum approximation, the closer the approximation will be to the exact area under the curve. As the width of each rectangle decreases, the sum of their areas approaches the actual area under the curve.

III. This statement is false. The midpoint sums method is not the average of the left sum and the right sum. Instead, it calculates the sum of the areas of rectangles using the midpoint of each subinterval.