Solving Anti-Derivatives for (x(x-4)^7) | Homework Statement

[A_Munk3y]

Homework Statement

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.

 

[lanedance]

Best check is to differentiate

 

[A_Munk3y]

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)

 

[lanedance]

What's the derivative of a constant?

 

[HallsofIvy]

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 $(1/9)(x- 1)^9+ (1/8)(x- 1)^8+ C$.

 

[Mentallic]

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.

 

[A_Munk3y]

The x is already "back": differentiate $(1/9)(x- 1)^9+ (1/8)(x- 1)^8+ C$.

(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)

 

[Mentallic]

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?

 

[A_Munk3y]

i actually assumed it should be equal :)
I'm really bad at simplifying, but i thought it should equal that.

 

[Mentallic]

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.

 

[A_Munk3y]

oh...

so then it would be u[x-1+1]?
then the -1 and 1 cancel out, and you get u[x]

 

[Mentallic]

Yep :tongue:

 

[A_Munk3y]

great! Thank you so much

 

[HallsofIvy]

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?

 

[A_Munk3y]

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.