The graph of is pictured below.Which of the following statements about are true?
i.A left endpoint approximation is greater than .II.A right endpoint approximation is less than .III.A trapezoidal approximation is less than

Question

​The graph of  is pictured below.Which of the following statements about  are true? ​  ​
i.A left endpoint approximation is greater than  .II.A right endpoint approximation is less than  .III.A trapezoidal approximation is less than  ​

Quizplus · Accepted Answer

I. From the graph, we can see that a left endpoint approximation would underestimate the integral, so it would be less than the actual value of the integral.

II. Similarly, a right endpoint approximation would overestimate the integral, so it would be greater than the actual value of the integral.

III. From the graph, we can see that the trapezoidal approximation would also overestimate the integral, so it would be greater than the actual value of the integral. Therefore, only statement III is true.

​The Graph of Is Pictured Below

The Graph of Is Pictured Below