Math 125       Test 4           8 points each          April 12, 2006

 

Integrate

 

1. º 5x dy

 

2.  º xy2 dy

 

3.   º sec x tan x dx

 

4.  

 

 

5.

 

6.  

 

7. 

 

8.  Find the differential dy for:

 

y = sin 2x2

 

9.   Suppose chicken profits obeyed the equation P =C3 /3 - 200 C2 + 40000 C - 500, where C represents the number of chickens raised).  How many chickens should be raised to maximize profits?

 

 

10.  A farmer wishes to build a rectangular shaped pen for her chickens with a fixed perimeter of 800 meters.   The pen is to have three equal sized pens.  Determine the dimensions of the pen that will maximize the area.

 

Find the area of the region bounded by

 

11.    y = x2 + x, y = 0, between x = 0 and x = 2

 

 

12.  y = x3 - x2 and  y = 0 between x = 0 & x = 3