Wetzel

Math 140

4.3 – Riemann Sums and Definite Integrals

 

Definite Integrals –

 

                                

 

 

            “The integral of f from a to b.”

 

            lower limit – a

 

            upper limit – b

 

            To Solve:  Fundamental Theorem of Calculus (4.4)

 

                       

 

           

 

 

            Example from 4.2

 

                       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Properties of Definite Integrals –

 

·        If f(x) is continuous on [a, b], then f(x) is integrable on [a, b].

 

·        If f(x) exists at x = a, then

 

                 

 

·        If f(x) is integrable on [a, b], then

 

                                   

 

·        If f(x) is integrable on [a, b] and c is in [a, b], then

 

                                   

 

 

 

Ex.:

1.)                                                                      2.) 

 

 

 

 

 

 

 

 

3.)                                                              4.) 

 

 

 

 

 

 

 

 

 

HW:  p.279  #23-43odd