# Properties of the definite integral.

Proposition 8.4.2   Let be a function integrable on an interval and let . Then:

Proposition 8.4.3   Suppose that the functions and are integrable on . Then is integrable on and:

Proposition 8.4.4   Suppose that the function is integrable on . Then is integrable on and:

Proposition 8.4.5   If is integrable on and if on , then .

Corollary 8.4.6   If and are integrable on and if on , then .

Corollary 8.4.7   If is integrable on , then is also integrable on and .

For definite integrals, the method of substitution (v.s. 2.2) is described as follows:

Theorem 8.4.8   Let be two numbers such that Let be a function having a continuous first derivative on and such that . If is a function, continuous on the interval , then for any we have:

In particular

Noah Dana-Picard 2007-12-28