Properties of Integrals

Properties of Integrals:

Different Properties of Integrals can be used to evaluate certain integral equations.

To evaluate an integral:

1. f(x) must be defined

2. The function must be continuous on the interval

Adding/Subtracting Integrals:

 Integrals with an interval of 0:

 Multiplying Integrals by a constant:

 Adding Integrals of adjacent intervals:

 Negative Integrals:

Example from textbook (pg. 290 #2):

a. (-2) ∫f(x)dx = (-2)(-1) = 2

b. ∫f(x)dx + ∫h(x)dx = 5+4 = 9

c. ∫[(2)∫f(x) - (-3)∫h(x)]dx

    (2)∫f(x)dx - (-3)∫h(x)dx = (2)(5)-(-3)(4) = 10+12 = 22

d. ∫f(x)dx = 1

e. (from 1 to 9)∫f(x)dx + (from 7 to 1)∫f(x)dx =  (from 7 to 9)∫f(x)dx =  

    -1 + -∫f(x)dx = 5

    5 +1 = 6

    -6 = (from 1 to 7)∫f(x)dx

f.  ∫h(x)dx - ∫f(x)dx = 4-5 = -1

*keep in mind that the intervals must be the same as what you are evaluating for as I could not type and show that here