Exercises
UF Calculus Set 31
1. The graph of a function
f
(
x
)
is given below. Estimate the area under the curve on the interval
using rectangles as directed. Assume each rectangle height is a multiple of 0.5.
(a) On the interval
[ 0
,
12 ]
using 4 subintervals of equal width and right endpoints as sam
ple points.
(b) On the interval
[ 0
,
12 ]
using 12 subintervals of equal width and right endpoints as sam
ple points.
(c) On the interval
[ 0
,
12 ]
using 6 subintervals of equal width and midpoints as sample
points.
(d) This curve was drawn so that it seems to form the hypotenuse of three right triangles.
Estimate the area this way; which approximation seems to be best of parts (a)(c) ?
2. An overhead image of a shoreline is given below. Each square of the grid represents a plot
that is
1000
feet by
1000
feet. Use rectangles to estimate the area of the region formed by the
body of water (shaded in blue) as directed.
(a) ...using 12 subintervals of equal width and left endpoints as sample points.
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 Spring '08
 ALL
 Calculus, Geometry, Angles, Leftwing politics, Political spectrum, Rectangle, Sample points, equal width

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