Valenica, Daniel – Homework 2 – Due: Sep 11 2007, 3:00 am – Inst: Cheng
2
2.
area
≈
60
3.
area
≈
58
4.
area
≈
57
5.
area
≈
59
Explanation:
With 10 equal subintervals and right end
points as sample points,
area
≈
n
f
(1) +
f
(2) +
. . . f
(10)
o
1
,
since
x
i
=
i
. Consequently,
area
≈
56
,
reading off the values of
f
(1)
,
f
(2)
,
. . . ,
f
(10)
from the graph of
f
.
keywords:
Stewart5e, graph, estimate area,
Riemannn sum
004
(part 1 of 1) 10 points
Estimate the area under the graph of
f
(
x
) = sin
x
between
x
= 0 and
x
=
π
4
using five approx
imating rectangles of equal widths and right
endpoints as sample points.
1.
area
≈
0
.
328
2.
area
≈
0
.
348
correct
3.
area
≈
0
.
388
4.
area
≈
0
.
368
5.
area
≈
0
.
308
Explanation:
An estimate for the area,
A
, under the
graph of
f
on [0
, b
] with [0
, b
] partitioned in
n
equal subintervals
[
x
i

1
, x
i
] =
h
(
i

1)
b
n
,
ib
n
i
and right endpoints
x
i
as sample points is
A
≈
n
f
(
x
1
) +
f
(
x
2
) +
. . .
+
f
(
x
n
)
o
b
n
.
For the given area,
f
(
x
) = sin
x,
b
=
π
4
,
n
= 5
,
and
x
1
=
1
20
π,
x
2
=
1
10
π,
x
3
=
3
20
π,
x
4
=
1
5
π,
x
5
=
1
4
π .
Thus
A
≈
n
sin(
1
20
π
) +
. . .
+ sin(
1
4
π
)
o
π
20
.
After calculating these values we obtain the
estimate
area
≈
0
.
348
for the area under the graph.
keywords:
estimate area, graph, Riemann
sum
005
(part 1 of 1) 10 points
Cyclist Joe accelerates as he rides away
from a stop sign. His velocity graph over a 5
second period (in units of feet/sec) is shown
in
1
2
3
4
5
4
8
12
16
20