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

Using the method of midpoint Reimann sums, approximate the integral of the function over the interval using four midpoints.

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

Use Riemann midpoint sums to approximate the area between the curve and the -axis between and . Use five intervals .

The derivative of an unknown function is , and there's a known function value at . Utilize the method of midpoint Riemann sums and Euler's method to approximate using four midpoints for the former and four steps for the latter.

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:

?

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

Using the method of midpoint Reimann sums, approximate the integral of the function over the interval using four midpoints.

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