- #1
Mattara
- 348
- 1
The task is to find one primitive function to:
[tex](4x-3)^2[/tex]
This was quite straightforward. Or so I though.
It can easily be turned into
[tex]16x^2 - 24x + 9[/tex]
and then integrated to
[tex] \frac {16x^3}{3} - 12x^2 + 9x[/tex]
choosing C = 0
Then I started to think. Couldn't this be integrated using the chain rule backwards (with lack of better wording)?
[tex](4x-3)^2[/tex]
then becomes according to my integration
[tex] \frac {(4x-3)^3}{12}[/tex]
If I differentiate the above, I get the initial function. What I'm having a hard time understanding is that the different approaches yields different results. I plotted both of them in my graph calculator and they indeed give different results.
Any hints on what I did wrong is greatly appreciated. Thank you for your time. Have a nice day.
[tex](4x-3)^2[/tex]
This was quite straightforward. Or so I though.
It can easily be turned into
[tex]16x^2 - 24x + 9[/tex]
and then integrated to
[tex] \frac {16x^3}{3} - 12x^2 + 9x[/tex]
choosing C = 0
Then I started to think. Couldn't this be integrated using the chain rule backwards (with lack of better wording)?
[tex](4x-3)^2[/tex]
then becomes according to my integration
[tex] \frac {(4x-3)^3}{12}[/tex]
If I differentiate the above, I get the initial function. What I'm having a hard time understanding is that the different approaches yields different results. I plotted both of them in my graph calculator and they indeed give different results.
Any hints on what I did wrong is greatly appreciated. Thank you for your time. Have a nice day.