- F(x) is the integral of f(x);
- F(b) is the value of the integral at the upper limit, x=b; and
- F(a) is the value of the integral at the lower limit, x=a.
Properties of the Definite Integral:
- Integral of a constant:
(b) if c is a constant.
- Interval Additivity
(c) If a < b then it is convenient to define
If 0 < f(x) < g(x) for all x in [a, b],
The Evaluation Theorem
If f is a continuous function and F is an antiderivative of f, F'(x) = f(x), then
Example: Using the Theorem, Find the value of .
- Applying what you learned, an antiderivative of x2 is
- Then, evaluate and substitute the limit.
= with limit 0 to 1 =
If you have some clarifications. Let me know.
credit: Renato E. Apa-ap, et al.