Math 106  Lab   M. Flashman
Friday April 23rd, 2004 11:00-11:50
Part I.Integration
• Enter and graph the function
• y = 4x -x2
• Integration : Integrate
• definite
• Estimate the definite integral of y = 4x -x2 from x=0 to x=2.
• Using left hand endpoint, n = 4, n= 10 and n =1000.
• Try some of the other numerical methods on the menu.
• indefinite
• Using the parameter C, find an indefinite integral for y = 4x -x2
• Graph your solution and use the family feature to show some of the  family of these solution.
• Use the indefinite integral feature to graph an indefinite integral for y = 4x -x2 from x=0, and then from x = 2 and x = 4.
• Compare the results of the previous two graphings.
• Find where the two graphs intersect.
• Use the integration on the two function menu to estimate the area of the region in the plane between these graphs with n = 4 , n= 10, and n=1000.
• Integration  f-g
•  Level curves
• Using Equ...implicit for z= 4x + 2y - 3xy
• Use C = 4x + 2y - 3xy then using the C animator you can see which (x,y) will give z = f(x,y) = C.

Part II  3-Dimensional Functions
• Point...
• Segment...
• Plane ...
• Explicit
z =f(x,y): cartesian coordinates
•   z= 4x + 2y - 3xy
z= ax + by - cxy