The general Riemann 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:

?

The general Riemann 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:

?

A Riemann Sum approximation of an integral follows the form

.

Where n is number of points/subintervals used to approximate the integral.

Knowing this, imagine a modified style of Riemann Sum, such 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 Riemann sums, approximate the integral using three midpoints.

Approximate the integral of for to using midpoint Reimann sums and three midpoints.

The velocity of an errant particle is given by the function . Approximate the average velocity of the particle over the interval of time using the method of midpoint Reimann sums and four midpoints.

Using the method of midpoint Riemann sums, approximate the integral using three midpoints.

Using the method of midpoint Reimann sums, approximate the integral using three midpoints.

The general Riemann 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 Riemann sums, approximate using two midpoints.