Exercises
UF Calculus Set 32
1. The graph of a function
f
(
x
)
is given below. Estimate the integral over the interval
[

4
,
8]
using a Riemann sum as directed. Assume each rectangle height is a multiple of 0.5.
(a) .
..using 4 subintervals of equal width and right endpoints as sample points.
(b) .
..using 12 subintervals of equal width and right endpoints as sample points.
(c) .
..using 6 subintervals of equal width and midpoints as sample points.
2. In each case, write the integral of the region as the limit of a Riemann Sum with intervals of
equal width and right endpoints as sample points.
(a)
Z
2
0
3
1 + 2
x
d
x
(b)
Z
2
1
p
1 +
x
2
d
x
(c)
Z
3
0
x
3

5
x
d
x
3. For the integrals in Exercise 2, approximate the value of each, using a Riemann Sum as di
rected.
(a) For the integral in part (a), use 4 equally spaced subintervals and left endpoints as sam
ple points.
(b) For the integral in part (b), use 4 equally spaced subintervals and midpoints. (Round the
answer to the nearest thousandth.)
(c) For the integral in part (c), use 6 equally spaced subintervals and midpoints as sample
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 Spring '08
 ALL
 Calculus, Geometry, dx, Riemann sum, Sample points

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