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Urgent! Calculus Help!

  1. Calculate L4 for f(x)=x^2-x+1 and 1<=x<=3. Furthermore, on the given axes, sketch the graph of f(x) and the rectangles corresponding to L4.

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I've answered 4 lengthy questions from you today and all except this one have been removed. What's going on?

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1 Answer

Break the interval 1≤x≤3 into 4 subintervals of length Δx=0.5, starting at 1, 1.5, 2, and 2.5. Find f(x)=x²-x+1 at these points:
f(1)=1,  f(1.5)=1.75,   f(2)=3,   f(2.5)=4.75.
 
Then the lower sum is
L4=(1+1.75+3+4.75)*0.5=5.25.
 
Notice how much the 4 rectangles underestimate the area under the graph, especially the rightmost one.