Math 1414-Online
Spring 2015
Efrain Guevara
This is a tentative calendar; the instructor may modify it according to the needs of the class. For a description of each section, please refer to our
syllabus.
Week
Mon-Sun
1/20-1/25
1/26-2/1
2/2-2/8
2/9-2/15
2
Indefinite Integral Quiz 13 - Solution
Evaluate cos2 x dx using integration by parts
Solution
cos
x dx sin x cos x sin 2 x dx sin x cos x sin 2 xdx sin x cos x 1 cos 2 x dx
2
sin x cos x 1 dx cos 2 x dx
sin x cos x x cos 2 x dx
u cos x
dv cos xdx
du s
Volume of a Cone Quiz Solution
Find the formula for the volume of a cone of radius r and height h using volumes of rotation.
Solution:
h
x (as shown to
r
the right). Rotate this region about the y-axis. If we build a rectangle perpendicular
to the y-axis
Volume of an Ellipsoid Quiz - Solution
x2 y 2
+
=
1 around the
a 2 b2
x-axis. Find a formula for the volume of this ellipsoid.
b
An ellipsoid is generated by rotating the ellipse
Solution:
y
=
a
b 2
a x2
a
Draw a rectangle at a point, x, on the x-axis. Th
Indefinite Integral Quiz 7 - Solution
Evaluate: sec3 d
You may use the fact that sec
d ln sec + tan
=
Solution:
d
sec =
3
u
du
sec tan sec tan 2 =
d sec tan sec ( sec 2 1)=
d sec tan sec3 d + sec d
sec
=
dv sec 2 d
sec
=
tan d v tan
So we have: sec3
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You may use the feiiowing integrais without deriving them:
{secxdx : lnksecx + tanxi
v‘
jcscxdx : Enicscx m mtxi
1‘ Set up the integral ta
Quiz of Volumes of Rotation
Consider the region bounded by y = cos x, the x-axis, and the
y-axis. The graph of this region is shown to the right.
a)
Which volume will be greater if this region is rotated
around the x-axis or the y-axis? Why?
b)
Compute th
Area Puzzle Quiz 2 - Solution
To the right is a graph of y cos x . Determine the
value of the constant, k, such that the area under the
curve from
2
curve from k to
to k is 3 times the area under the
.
2
k
2
Solution:
The area under the curve from
2
k
t
Improper Integral Quiz 3 - Solution
arctan x
and above
x2
the x-axis between x = 1 and x = .
Find the area under the curve y =
Solution:
a
arctan x
x
arctan x
arctan x
dx
lim
dx
lim
ln
=
=
+
1 x 2
2
a
a
x2
x
1+ x
1
arctan a
a
lim
+ ln
2
a
a
1+
Chapter 3
Kinematics in Two or Three
Dimensions; Vectors
Homework
Tuesday:
Read Chapter 4
2014: Do P. 77 1,2,4,5,11,12,13,14
2013: Do p. 77 1, 2, 4, 5, 18
2012: Do p. 77 1, 2, 4, 5, 11, 12, 13, 14, 17
How do we calculate the
motion of this skier in two
di