The equations are and .

Consider .

Area of the region:

If is continuous and non-negative on the closed interval , then the area of the region bounded by the graph , the -axis and the vertical lines and is given by area.

The area of the region is .

The number of subintervals are .

Width .

Substitute and .

.

.

Find the function values:

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Simpsons rule :

.

.

The area of the region using Simpsons rule is square units.

The area of the region using Simpsons rule is square units.