Properties of Definite Integrals

We look at some properties of definite integrals and understand why they are true by visualizations and by going back to the definition of definite integrals.

This video is part of a lesson series in Integral Calculus for my Grade 12 students in the Philippine Science High School Main Campus.

00:00 Introduction
00:21 The definite integral switches its sign when the limits of integration are swapped
01:57 The definite integral is zero if evaluated in an interval with length zero
02:56 The definite integral of a constant is the constant multiplied to the length of the interval
03:51 The definite integral of c(f(x)) is equal to c times the definite integral of f(x)
05:02 The definite integral of sums and differences are the sums and differences of the definite integrals
08:02 The definite integral from a to c + the definite integral from c to b = the definite integral from a to b
11:23 If f(x) is above the x-axis in the interval, the definite integral is positive
12:10 If f(x) is greater than g(x) in the interval, then the definite integral of f(x) is greater than the definite integral of g(x)
13:20 Property if f(x) is between two constants in the interval