Definite Integrals — Part 1: Evaluation, substitution and basic properties: visual lesson, ISC Class 12 Mathematics

Lesson

Definite Integrals, Part 1

An indefinite integral is a family of functions; a definite integral is a single number.

In this lesson you will

Evaluate definite integrals with the fundamental theorem of calculus (stated without proof)
Change the limits when using a substitution
Use the dummy-variable, reversal and splitting properties
Integrate modulus and greatest-integer functions by splitting the interval

Part 1 at a glance.

Concept

Concept

If $f$ is continuous on $[a, b]$ and $F' = f$ , then $\displaystyle\int_a^b f(x)\,dx = F(b) - F(a)$ . (The proof is not in the ISC syllabus.)

\int_a^b f(x)\,dx = \Big[F(x)\Big]_a^b = F(b) - F(a)