Math 21
Exam 4
1. (16 points) The curve
C
is given by the parametric equations,
x
=
e
t
.
y
=
√
t
, with
t
∈
[0
,
1].
a)
C
is also given by the Cartesian equation
y
=
F
(
x
), for
x
∈
[
c, d
]; where
F
(
x
) =
c
=
d
=
b) Give, but do not
evaluate, an integral that give the length of
C
. The limits of integration and the
integrand must be explicit, the integrand containing only the variable of integration.
Length =
c) Give, but do not
evaluate, an integral that gives the area of the surface obtained by revolving
C
around
the
y
axis. The limits of integration and the integrand must be explicit, the integrand containing
only the variable of integration.
Area =
2. (14 points) Let
R
be the region bounded by
y
= cos
x
,
x
= 0,
x
=
π
, and
y
= 0. Let
ρ
= 2. The
coordinates, (¯
x,
¯
y
), for the centroid of
R
are given by
¯
x
=
M
Y
M
¯
y
=
M
X
M
Give, but do not
evaluate, the integrals for
M
,
M
X
, and
M
Y
. The limits of integration and the integrand
must be explicit, the integrand containing only the variable of integration.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '98
 MathDep
 Calculus, Equations, Parametric Equations, 14 points, integrand

Click to edit the document details