Math 166 A2 Homework

Name:_ _ _ _ _ _ _ _ _ _ _ _ _ _ _

A copy of this assignment is available in the "Burkardt" folder for Math 166.
You may do this assignment with pencil and paper, calculator, or with Mathematica.

1.  Estimate the integral of the following function from 0  to 1.   Work directly from 
the graph.  Please show your computations.  You should report the values of 
the Right Riemann sum, the Left Riemann sum, the Midpoint rule and the Trapezoidal rule.

This is the formula that produced the graph.  You do NOT need it for your work!

f[x_]:=x+5*Sin[Pi*x^2]/Sqrt[x+3]

Plot[f[x],{x,0,1},GridLines->Automatic]

Right Riemann Sum = __________
Left Riemann Sum =   __________
Midpoint Rule=           __________
Trapezoid Rule=          __________

2.  Estimate the area of the region contained within the following shape using
any rule you wish.  Please state which rule you used, and show your computations.
You may completely ignore the "gibberish" below which produced the plot.

Clear[i,shape,x,y,y1,y2]
x=Table[Abs[i-11]/5,{i,1,21}];
y1=Table[ Sin[x[[i]]],{i,1,11} ];
y2=Table[ Sin[2]*x[[i]]^2/4,{i,12,21}];
y=Join[y1,y2];
shape=Table[{x[[i]],y[[i]]},{i,1,21}];

ListPlot[shape, PlotJoined->True, GridLines->Automatic]

Area estimate is:__________using the ___________ rule.


Now integrate in the y direction!  Show your computations:


Area estimate is:__________using the ___________ rule.