Math Help

Properties of Integrals

In a Nut Shell: Properties of integrals falls into two categories - standard properties (Table 1)

and comparison properties (Table 2). These properties help you evaluate integrals (standard

properties) or determine bounds on integrals based on the function or functions underneath the

integral and the limits of integration (comparison properties).

Table 1 Standard Properties of Integrals

∫ c dx = c ( b ˗ a ), where c is any constant

b b b

∫ [ f(x) + g(x) ] dx = ∫ f(x) dx + ∫ g(x) dx

a a a

b b

∫ c f(x) dx = c ∫ f(x) dx where c is any constant

a a

b b b

∫ [ f(x) - g(x) ] dx = ∫ f(x) dx - ∫ g(x) dx

a a a

c b b

∫ [ f(x) dx + ∫ f(x) dx = ∫ f(x) dx

a c a