# Area and fundamental theorem

http://img521.imageshack.us/img521/4549/bbav9.png [Broken]

The problem states that it wants the upper and lower estimate of total distance. Therefore, I used rectangles to solve for it. However, let's say I'm working on upper limits. For my initial rectangles, I use the right endpoints, but then it begins to slope downward, so at that point, if I use right endpoints, I am below the graph. Do I continue using right endpoints, or do I switch to left endpoints to have my rectangles stay over the graph?

http://img521.imageshack.us/img521/22/bb2by3.png [Broken] <--I forgot to put on there that this curve = f(x)

This problem states... for each quantity in questions a-d, copy the diagram and show the quantity on the diagram. Explain what the expression means in terms of the graph. Note that F'(x) = f(x).

For example if the question showed the quantity square root of (b-a)^2 + (f(b)-f(a))^2 then you would explain that this is the distance on PQ and you would draw a line segment PQ on the diagram.

a) f(b)-f(a)

b) f(b)-f(a)/b-a

c) F(b) - F(a)

d) F(b) - F(a)/b-a

I have no idea how to start this.. b and d both seem like slope equations to me, but I don't know the difference.

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Gib Z
Homework Helper
1st problem, switch. Or better, use midpoint rectangles, or simpsons rule.

2nd part,

a) part a perpendicular line, long enough to cross the segment from B(b) to q. The distance from the point of intersect, and q, is what you want.