Anti-deriv (x(x-4)^7)

  • Thread starter A_Munk3y
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  • #1
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Homework Statement



m31n8.jpg





The Attempt at a Solution


Sorry, i didn't know how to put this on the forum so i did it on paint and uploaded it to tinypic.


Here is the image of the "attempted" solution.
149yt6d.jpg
 

Answers and Replies

  • #2
lanedance
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Best check is to differentiate
 
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  • #3
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Oh, ok, but how do i differentiate the c and what do i do to bring back the x when i differentiate? (since i changed the x to u+1)
 
  • #4
lanedance
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What's the derivative of a constant?
 
  • #5
HallsofIvy
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Oh, ok, but how do i differentiate the c and what do i do to bring back the x when i differentiate? (since i changed the x to u+1)
The x is already "back": differentiate [itex](1/9)(x- 1)^9+ (1/8)(x- 1)^8+ C[/itex].
 
  • #6
Mentallic
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I'll be frank here, if you don't know what to do with the c then you probably don't have a clue why you put it there in the first place. You should go back and read up on the fundamentals of integration.
 
  • #7
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The x is already "back": differentiate [itex](1/9)(x- 1)^9+ (1/8)(x- 1)^8+ C[/itex].
(x-1)8+(x-1)7 => (x-1)7x (im guessing the c is a constant?)

I'll be frank here, if you don't know what to do with the c then you probably don't have a clue why you put it there in the first place. You should go back and read up on the fundamentals of integration.

we never learned the fundamentals of integration :)
We are going to learn them today, this is just a problem she gave us and said to try to solve it on our own. (like a heads-up kind of thing)
I just looked up an example and tried to copy it and i really have no idea what c is. (so i guessed :D)
 
  • #8
Mentallic
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Oh ok, in that case, yes the c is just a constant so whenever you take the derivative of a constant it is always 0.

Ok so are you satisfied? Did you get from (x-1)8+(x-1)7 => x(x-1)7 by some process or did you just assume it should be equal?
 
  • #9
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i actually assumed it should be equal :)
I'm really bad at simplifying, but i thought it should equal that.
 
  • #10
Mentallic
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Well since you have two factors, (x-1)8 and (x-1)7 and you need to get to 1 factor, then you should factorize! Letting (x-1)7=u will make things a lot more easy to spot.
 
  • #11
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oh....

so then it would be u[x-1+1]?
then the -1 and 1 cancel out, and you get u[x]
 
  • #12
Mentallic
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Yep :tongue:
 
  • #13
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great!! Thank you so much :biggrin:
 
  • #14
HallsofIvy
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Why were you "guessing" that C was a constant? You were the one who put it in there weren't you? What did you think it was when you added it to the solution?
 
  • #15
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i wasn't sure. Like i said, i had never done integrals before so i just looked at another problem and tried to copy the steps that it took to solve. Constant made the most sense so that's what i guessed it was.
 

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