Consider the function between and . Find the definite integral using midpoint Riemann sums with two rectangles.

Find the derivative of the following function

The general Reimann Sum approximation of an integral takes the form

Where is the number of points/subintervals, and each subinterval is of uniform width .

Knowing this, imagine that the subintervals are not of uniform width.

Denoting a particular subinterval's width as ,

the integral approximation becomes

Which of the following parameters would give the closest integral approximation of the function:

?

Using the method of Midpoint Reimann sums, approximate the integral of over the inteval using two midpoints.

Utilize the method of midpoint Riemann sums to approximate using three midpoints.

This table gives values of a function at certain values of .

Using the table above, find the midpoint Riemann sum of with from to .

Determine the slope of the line that is tangent to the function at the point

Utilize the method of midpoint Riemann sums to approximate using three midpoints.

Find the derivative of the function.

Find the derivative of .