.

The function is .

Find the actual value.

.

Find .

.

Calculate the at the interval boundaries.

.

(a)

Find Trapezoidal Rule approximation and error .

The error

.

Find Simpson Rule approximation and error .

The error

.

Find Midpoint Rule approximation and error .

.

The first mid point is .

Calculate the at the interval boundaries.

.

The error

.

(b)

The magnitudes of the actual errors are less than the estimates.

.

(c)

Trapezoidal rule:

Midpoint rule:

Simpson rule:

.

(a) , ; , and , .

(b) ; ; .

(c) for ; for ; for .