Integral of a Constant Function

Given a constant c > 0, evaluate the integral

Figure 4.1.13

Figure 4.1.13 shows that for every positive real number Δx, the finite Riemann sum is

Figure 4.1.14

By the Transfer Principle, the infinite Riemann sum in Figure 4.1.14 has the same value,

.

Taking standard parts,

.

This is the familiar formula for the area of a rectangle.