Want to win a PS4? Go Premium and enter to win our High-Tech Treats giveaway. Enter to Win

x
?
Solved

Integral of 4/x

Posted on 2011-03-07
3
Medium Priority
?
427 Views
Last Modified: 2012-05-11
I understand that the integral of 1/x is ln x + c where x > 0
but what happens if you integrate 4/x?

Is it 4.ln x + c?

I'm not sure where the 4 fits in to the answer.
0
Comment
Question by:purplesoup
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
3 Comments
 
LVL 6

Accepted Solution

by:
akajohn earned 1200 total points
ID: 35055352
I hope I can make this clear

4 * 1/x

Integrate and you get


4 ln x + k

Here my constant K is arbirtrary and is equal to 4*c.

4 times a constant is just another constant.

Does that help?
0
 
LVL 18

Assisted Solution

by:deighton
deighton earned 400 total points
ID: 35056040
an example is say, integrate 1 / (2x)

by substituting
u = 2x
du = 2dx
dx = du/2

you can get

(1/2) ln(2x) + c

if you differentiate that, you get

(1/2) 2 / 2x = 1/(2x)

however, note that

(1/2) ln(2x) + c = (1/2) (ln(x) + ln(1/2)) + c = (1/2) ln(x) + (1/2) ln(1/2) + c

=  (1/2) ln(x) + k

absorbing the term into another arbitrary constant in that case.

0
 
LVL 32

Assisted Solution

by:phoffric
phoffric earned 400 total points
ID: 35056197
In general, for any constant b:
     § b f(x) dx = b § f(x) dx
i.e., you can bring the constant factor outside of the integral.

You may have already seen that the integral can be used to calculate the area under a curve. So, if you calculated the area under the function f(x) in some interval, then if you consider another function g(x) = 2 f(x), then g(x) is twice the value of f(x) for any particular x. Then you would expect that the area under the curve g(x) to be twice as much as the area under the curve f(x).

For your indefinite integra, if
     § f(x) dx = h(x) +c
then from above, you would say
     § b f(x) dx = b § f(x) dx = b( h(x) +c ) = b h(x) + b c
where h(x) is just the integral of f(x)

But since b and c are both constants, you can just treat them as a single constant, call it C.
     § b f(x) dx = b h(x) + C


0

Featured Post

Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

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

Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! https://www.google.com/about/careers/students/guide-to-technical-development.html How to Know You are Making a Difference at EE In August, 2013, one …
This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
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.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

636 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