Calculus

Lesson 20 Antiderivatives

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                         is the "Antiderivative" of  when .

                        Find :         

                        What about adding a constant?  If  and , note that

                        they have the same derivative.

                        So if , then , where we

                        call  the "constant of integration."

            So, here is the proper way to solve for a function, given its derivative:

            Always think:  what would I have to differentiate to get this function? 

            Two ways to think about it:         

                                    More exmples:        

            Sometimes you may have to re-write the polynomial or trig function:

            Finally, note that , thus far, could be anything.  (Plot  which

                        is the antiderivative of  since

                        ).

            Pick an initial condition to solve .  For instance, let's say that we knew that .

            REALLY FINALLY, solve the differential equation:

On to Lesson 21 - Area

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