1.         Evaluate the integral:

         2.         Find y = f(x) if f"( x) = x + 2, f'(0) = 3, f(0) = -1

         3.         Use the formulas to find

         4.         Use a calculator method to find the area under the graph  y=1- x² over [-1, 1].  Explain the method and the steps used to find area.

          5a)     Use a geometric formula to find the value of .  Draw a figure, give exact value.    

             b)    Use the "calc" function of the calculator to find the approximate area.  (Use this as a check!)

         6.         Given    , and  .         

                     Find:          a)                           b)                    c) .          

         7.         Evaluate the definite integral (by algebraic process):

                     .  Check by calculator methods.  Explain how.

         8.         Given  , find F'(x).

         9.         Find the average value of f(x) = sin x on [0,π].

                     [Hint:  Use unless you know a better way.] 

       10.         Draw a sketch, use the calculator and find the area under the curve for using:

                     a)    Left rectangles with  n = 4

                     b)  Right rectangles with  n = 4

                     c)  Trapezoidal Rule with  n = 4

                     d)  Simpson's Rule with  n/2 = 4 

                     e)  Simpson's Rule with    n = 4

                      f)  Trapezoidal Rule with  n = 20.         

                     g)  Integration function of the calculator.

       11.         Find the exact area (in radical form) of by  integration methods.

 In 12 - 14, evaluate the integrals.

       12.                     

       13.       

       14.