Problem 1 

f[x_]:=x^3+2*x;  a=-1; b=3;
FilledPlot[f[x],{x,a,b},AspectRatio->1]

[Graphics:../Images/quiz6-answers_gr_1.gif]

INT=Integrate[f[x],{x,a,b}]
[Graphics:../Images/quiz6-answers_gr_2.gif]
n=2;
LEFT[n]=LeftEndpointRule[f,{a,b,n}]
[Graphics:../Images/quiz6-answers_gr_3.gif]
RIGHT[n]=RightEndpointRule[f,{a,b,n}]
[Graphics:../Images/quiz6-answers_gr_4.gif]
TRAP[n]=TrapezoidRule[f,{a,b,n}]
[Graphics:../Images/quiz6-answers_gr_5.gif]
MID[n]=MidpointRule[f,{a,b,n}]
[Graphics:../Images/quiz6-answers_gr_6.gif]
SIMP[n]=SimpsonRule[f,{a,b,n}]
[Graphics:../Images/quiz6-answers_gr_7.gif]

Converted by Mathematica      February 22, 2001