




[1]  (a)(#37 Pg 420, 3 numbers changed, method same)(3 pts) Find  ( 2x  4 )^{6}  dx  

u = 


y(u) = 

(b)(#37 Pg 420 cont'd)(2 pts) Show that 

( 2x  4 )^{6}  dx  = 
64 7 
[2] 
(a)(part of #21 Pg 451)(3 pts) On the figure at the right are the
graphs of [ y = 7250  18x^{2} ] and [ y = 3620 + 12x^{2} ]. 

Without using a graphing calculator, express the area shaded at the right as a single definite integral by entering specific integers (such as 3, 2, or 0) in the 5 empty answer boxes below. Show some algebraic work, especially in finding the two limit numbers immediately to the right of the integral sign, but you need not find the value of above integral.  


(b)(more of #21 Pg 451; you may use a calculator ONLY to add and multiply)(2 pts, for work only) Evaluate the integral in [2](a) above, and thus discover that the area shaded in the figure above is exactly 26620. 
[3] 



[4] 


Your answer will be an equation with no "x" on the left side, and no "y" on the right side. Your answer should not contain y'. For example, the GENERAL SOLUTION of [ y' = 2x ] is [ y = x^{2} + C ].  






[6] 
(#3 Pg 584, voted in) Use least squares method to find the line best
fitting the data points : (1,2) , (2,4) , (4,4), and (5,2) 
[7]  (a)(Pg 572 #9, 2 numbers changed)(2 pts) Find f_{x} , f_{y} , f_{xx} , f_{xy} , and f_{yy} where f(x,y) = x^{3}  4xy + y^{3} .  
(b)(more of Pg 572 #9)(1 pt) Show algebra work used to find the critical points (CP's) for the function f(x,y) in (7a) above. The CP's are given in the table below.  
(c)(rest of Pg 572 #9)(2 pts) Complete the table below using your results in (7a) and (7b) above:  






The algebra and calculus are fairly easy. Credit only for work. Note [C] at top of test. 
[9] 



