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pproximation to the net area by counting the number of rectangles (and
 parts of rectangles) under the graph that are above the axis, and sub
tracting the number that are below the axis .  The calculus approach b
egins with a variant of this simple idea: we approximate the required \+
area by rectangles.  More explicitly, we divide the interval [-1, 4] i
nto some number of equal sub-intervals, and then draw a rectangle over
 each sub-interval whose height is the height of the graph at the righ
t-hand endpoint of the sub-interval.  We can draw the rectangles by ta
king advantage of " }{TEXT 257 7 "Maple's" }{TEXT -1 1 " " }{TEXT 258 
8 "rightbox" }{TEXT -1 26 " command, which is in the " }{TEXT 259 7 "s
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s example, we used 6 sub-intervals.  (That's what the last argument in
 the " }{TEXT 256 8 "rightbox" }{TEXT -1 117 " command is for.)  We ca
n add up the areas of the 6 rectangles easily enough (note that each r
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y that this computation by itself will give a very good approximation \+
to the area under the graph.   To get a better approximation, we could
 try using more rectangles.  Here are the picture and the sum with 12 \+
rectangles (each of which will then have base length 12/5):" }}}
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urve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve
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