This preview shows pages 1–2. Sign up to view the full content.
When and how do I “set up” an integral?
1.
Determine that an integral needs to be done.
If you pay attention to what you are doing you will always recognize the
need to integrate due to the fact that some quantity in a formula you are trying to use has a variable value.
For instance:
t
=
d
v
applies to an object moving at constant speed, but what if the speed is not constant over the distance
d
?
In this case
there is no obvious single value of
v
to use. Similarly
F
=
Gm
1
m
2
d
2
applies to two point objects separated by a distance
d
, but
what if one or both objects have spatial extent?
In this case there is no obvious value of
d
to use.
Case 1:
The gravitational force due to a uniform ring of radius
R
and mass
M
on a particle of mass
m
located on its axis at a
distance
x
from its center.
M
m
x
R
Case 2:
The time required for an object
to travel a distance
d
from
rest if
v
=
a
+
bx
+
cx
2
where
a
and
b
are constants and
x
is the distance from the original location.
2.
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.
 Spring '08
 IdontKnow
 Physics

Click to edit the document details