Important things to remember from Calc 1 as you begin Calc 2. Remember the main goal of 
       Calculus 2 is to learn different techniques and applications for integration.  
                                           
        
        
        
                 Anti-Derivatives 
                     •   In calculus, an antiderivative, inverse derivative or indefinite integral of a function f is a 
                         differentiable function F whose derivative is equal to the original function f. This is the 
                         building blocks of taking an integral and  is important to remember as the basics for this 
                         course. 
                  
                 Integration 
                     •   The process of finding the area under the curve. (This will be the main topic of Calc 2) 
                     •   + C is added to the end whenever the bounds are not known (Indefinite Integral). This is 
                         called the arbitrary constant. 
                     •   Some important integrals to know are: 
                             o  Integrals of trig functions (Sin,Cos,Tan,Csc,Sec,Cot,Sec^3(Secant cubed)) 
                 U Substitution 
                     •   A way of breaking down an integral in order to make it something we know how to 
                         handle. 
                     •   We can change the bounds when we do this by plugging the bounds in for X in our U 
                         sub. 
                             o  This does not HAVE to be done if you do not want to BUT you will have to 
                                 substitute everything back (Change the U back to X) if you do not change 
                                 bounds. 
                                                                                                                       
                  
                  
                  
                  
                  
                  
                  
                  
                  
                 Derivatives 
                     •   Product Rule 
                                                                                  
                     •   Quotient Rule 
                                                                                        
                     •   Chain Rule 
                                                                                                           
                     •   Memorize Trig Derivatives 
                             o  See chart above to see the trig derivatives but I highly recommend knowing the 
                                 trig derivatives and trig integrals. 
                          
                 Graphing Using Derivatives 
                          st
                     •   1  Derivative is Slope at that point (+ = Upward slope, - = Downward Slope, 0 = turning 
                         point) 
                          nd
                     •   2  Derivative is Concavity ( + Concave up, -  Concave down) 
                             o  If 0 for the purpose of the second derivative test it would be inconclusive. 
                     •   Using this idea beyond graphing – Finding Mins and Maxes 
                             o  This is used in Physics more than Calc but we use derivatives and how they 
                                 influence our graph to find our minimums and maximums.  
                             o  To do this we take the derivative of the function and set it equal to 0. This will 
                                 give us our GLOBAL min or max. 
                 Relationships of Derivatives 
                     •   This is in respect to taking the derivative of position(x) with respect to time(t) 
                          st
                     •   1  Derivative is Velocity  
                          nd
                     •   2  Derivative is Acceleration  
                          rd
                     •   3  Derivative is Jerk 
                 Fundamental Theorem of Calculus  
                     •   The fundamental theorem of calculus is a theorem that links the concept of differentiating 
                         a function with the concept of integrating a function.