Solved

Vector Calculus: Indefinite Integral of a Vector

Posted on 2011-09-20
6
377 Views
Last Modified: 2012-05-12
r''(t) = -t^(-2) i, t > 0
r'(1) = i + j
r(1) = j

Find r(t).

My question is, how do I find C when I take the indefinite integrals?
So far i have:
r'(t) = t^(-1)i + C ==> C = j
&
r(t) = ln(t)i + tj + C ==> C = 0k but I'm not sure if it's right, or how to check if I am right. Any help is (as always) much appreciated.
0
Comment
Question by:Zenoture
6 Comments
 
LVL 84

Assisted Solution

by:ozo
ozo earned 166 total points
ID: 36571694
adjust C to make r(1) = j
0
 

Author Comment

by:Zenoture
ID: 36571752
Why?
If r(t) = ln(t)i + tj + C, then
r(1) = j = ln(1)i + (1)j + C
   j = 0i + j + C
   j = j + C
   0 = C

But that just means we can ignore C doesn't it?
0
 
LVL 84

Expert Comment

by:ozo
ID: 36571770
Do you usually ignore parameters when their value is 0?
0
Problems using Powershell and Active Directory?

Managing Active Directory does not always have to be complicated.  If you are spending more time trying instead of doing, then it's time to look at something else. For nearly 20 years, AD admins around the world have used one tool for day-to-day AD management: Hyena. Discover why

 

Author Comment

by:Zenoture
ID: 36571774
Yes
0
 
LVL 27

Assisted Solution

by:BigRat
BigRat earned 167 total points
ID: 36572875
All I can say is tsk,tsk. When one plays with differential equations, each integration introduces a new constant. I always call then A,B,C,... so as to avoid confusion.

So the first integration introduces A which turns out to be 1. And the second integration introduces B which turns out to be 0.

Furthermore if we are dealing with three dimensions i,j and k, then the first integration introduces A and B, and the second C and D. This keeps things clean and avoids confusion.
0
 
LVL 18

Accepted Solution

by:
deighton earned 167 total points
ID: 36573133
r'(t) = (1/t) i + Ai + Bj

r'(1) = i + j
hence A = 0 B = 1

so

r'(t) = (1/t) i  + j

r(t) = log(t) i + tj + Ci + Dj

r(1) = j

so C and D are zero

r(t) = log(t)i + tj



0

Featured Post

Three Reasons Why Backup is Strategic

Backup is strategic to your business because your data is strategic to your business. Without backup, your business will fail. This white paper explains why it is vital for you to design and immediately execute a backup strategy to protect 100 percent of your data.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Solving an equation 8 63
Geomentry-Fundamental concepts 6 66
Geomentry-Fundamental concepts-Angles 3 72
Does a rhombus have 2 pairs of parallel sides 5 65
Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

810 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question