Example 4

EXAMPLE 4

Figure 4.2.10

Find (Figure 4.2.10). The function √t is defined and continuous on the half-open interval [0, ∞]. But to apply the Fundamental Theorem we need a function continuous on an open interval that contains the limit points 0 and 4. We therefore define

This function is continuous on the whole real line. In particular it is continuous at 0 because if t ≈ 0 then f(t) ≈ 0. The function

is an antiderivative of f. Then

In the next section we shall develop some methods for finding antiderivatives. The antiderivative of a very simple function may turn out to be a "new" function which we have not yet given a name.