Question

I have a brief conceptual question! When evaluating Volumes of Solid of Revolution, and the following mathematical circumstance arises, within the integral...
4 - 4x^(-1)
... Which of the following should it be rewritten as?
1. 4 - 4(ln(x))
2. 4 - ln(4x)
3. Or something completely different(?)

Any and all help is greatly appreciated! :)

Answer 1

\[\int\limits_{}^{}4-4x^{-1}\]\[\int\limits_{}^{}4-\frac{ 4 }{ x }\]\[\int\limits_{}^{}4-4\int\limits_{}^{}\frac{ 1 }{ x }\]\[4x-4\int\limits_{}^{}\frac{ 1 }{ x }\]\[4x-4(\ln (x))+C\]
or:\[4(x-\ln (x))+C\]



ANSWER:\[4x-4(\ln(x) )+C\]

Answer 2

So, if there is a coefficient to the variable that is to the negative first– therefore meaning the anti-derivative of said variable is "undefined", or 0– you detatch the coefficient from the variable when rewriting the term(s) as a natural log, taking the log of only the variable itself (with the given number or limit plugged in of course)??

Answer 3

Simply put, and when analyzing THIS situation only, is "4 - 4x^(-1)" equal to "4 - 4(ln(x))" or "4 - ln(4x)" ?
Thank you!

Answer 4

@ganeshie8 Help Please?!? :D

Answer 5

\[\int 4 - \dfrac{4}{x} dx = 4x - 4\ln |x| + C \]

Answer 6

we're done with integration/calculus part.

Answer 7

if you prefer, u can write the answer as :

\[ 4x - 4\ln |x| + C = 4x - \ln |x|^4 + C \]

Answer 8

^^thats just based on a log property :
\[m \log n = \log n^m\]

Answer 9

I'm not sure if i have answered ur question...

Answer 10

Yes, you have! Thank you very much!

Answer 11

np :)

Answer 12

https://www.youtube.com/watch?v=iNtMLGvzFHA

Answer 13

i think u may like watching that funny debate on derivatives Vs integrals... when u have time :)

Answer 14

Alright, I'll check it out;)