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Original Message (ID '243128') By Bill Simpson:
Show your {x,f[x]} points to make absolutely certain that you are getting a Left sum In[1]:= f[x_]:=x^3-6x; a=0;b=3;n=6; p=Table[N[{x,f[x]}],{x,a,b-(b-a)/n,(b-a)/n}] Out[3]= {{0.,0.},{0.5,-2.875},{1.,-5.},{1.5,-5.625},{2.,-4.},{2.5,0.625}} Plot those points over the function to make absolutely certain the points are correctly on the function. In[4]:= Show[ListPlot[p, PlotStyle->{PointSize[.05]}], Plot[f[x], {x, a, b}], PlotRange->All] Out[4]= <<>> Total the sequence to get the left sum. In[5]:= N[Sum[f[x]*(b-a)/n,{x,a,b-(b-a)/n,(b-a)/n}]] Out[5]= -8.4375` Now try to desktop publish your expression so you can see the Sigma that I think you want. This almost certainly will not correctly display in your notebook. So follow these instructions to get it into your notebook. 1: Use the basic palette to enter the Sigma. 2. use the keyboard to enter x Tab a Tab b-(b-a)/n Tab f[x]*(b-a)/n= N[Sum[f[x]*(b-a)/n,{x,a,b-(b-a)/n,(b-a)/n}]] to fill in the little boxes and use your expression. 3.Position the cursor just before that N, press the left mouse button and drag to the right end of that. Release the mouse button and then press which, if a miracle happens and all this is correct and nothing goes wrong, should replace your N[Sum[f[x]*(b-a)/n,{x,a,b-(b-a)/n,(b-a)/n}]] with -8.4375` (where that trailing ` is indicating an approximate decimal number and can be ignored) but still leave your Sigma notation. If the very next thing you click is Edit and then Undo you can reverse this replacement. You can try to use the same click-n-drag-n-ctrl-shift-enter method to replace you a and b above and below your sigma, but I question whether the result will be what you really want. I also urge you to avoid using decimal points in your numbers, especially for your a,b,n because tiny round off errors may give you one too few or one too many terms in your sum.