# AP Calculus AB : Definite integral as a limit of Riemann sums

## Example Questions

### Example Question #1 : Definite Integral As A Limit Of Riemann Sums

True or False: If  is a negative-valued function for all ,

False

True

True

Explanation:

This is true. Since  is negative-valued, its graph is below the -axis, and the Riemann sums used to evaluate the area between  and the -axis have a negative value for height.

### Example Question #72 : Integrals

is a continuous function on the interval  and is differentiable on the open interval .  If , then which of the following statements MUST be true:

over the interval .

over the interval .

at some point , where .

at some point , where .

over the interval .