Sums to Integrals Laboratory

Problem #1

The formula to represent a function f with inputs x and y and output z is f (x, y) = x and were looking for the volume under the surface f and above the region .

Place the cross section for x = 0 and x = 2 on your kit.

Use these two cross sections to construct two prisms which extend the area between the xy plane and the curve on the left to the right endpoint. The first from of these prisms will go from x = 0 to x = 2 and the second from x = 2 to x = 4.

Approximate the volume by using the approximation Volume = .

Place the cross section for x = 0, x = 1, x = 2 and x = 3 on your kit.

Use these two cross sections to construct two prisms which extend the area between the xy plane and the curve on the left to the right endpoint. The first from of these prisms will go from x = 0 to x = 1 and the last goes from
x = 3 to x = 4.

Approximate the volume by using the approximation Volume = .

Use the Fundamental Theorem as you make the divisions smaller and smaller to find the precise volume.