Study Sheet for Test 3
MAC 3473, Honors Calculus 2
Keesling
Test on 4/19/11
1.
Determine the area of the circle using the polar coordinate parameterization
!
!
=
!
for
0
≤
!
≤
2
!
.
2.
Determine the arc length of the cardioid for the parameter range
0
≤
!
≤
2
!
.
The cardioid is parameterized by the following equation in polar coordinates.
Also determine the area under within the cardiod.
!
!
=
!
∙
1
−
cos
θ
3.
Determine the centroid of the following figures.
(a)
The area under the curve
!
!
=
!
!
over
0
,
1
for
!
=
0
,
1
,
2
,
3
…
.
(b)
The area under the curve
!
!
=
!
!
−
!
!
over the interval
[
0
,
!
]
.
(c)
The area under the curve
!
!
=
sin
(
!
)
over the interval
[
0
,
!
!
]
.
4.
Determine the centroid of the following curves.
[Note:
this is not the area under
the curve, but just the curve itself.]
(a)
The curve
!
!
=
!
!
over the interval
[
0
,
!
]
.
(b)
The curve
!
!
=
!
!
−
!
!
over the interval
[
0
,
!
]
.
5.
A semicircular dam holds back fresh water.
The level of the water held back is at
the top of the dam.
What is the total force of the water on the dam?
The
dimensions and shape of the dam are below.
Assume that the radius
!
=
750
!"
.
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 Spring '08
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 Calculus, Arc Length, Cone, Fractal

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