SOLUTION: Find all the antiderivatives for the following function. Check your work by taking the derivative.   f(y)= − 8/y^9 (use C as the arbitrary constant)

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Question 1156762: Find all the antiderivatives for the following function. Check your work by taking the derivative.
  f(y)= − 8/y^9
(use C as the arbitrary constant)
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

Anti-derivative is


    F(y) =  + ,


where " C " is an arbitrary constant.


It is "a Table integral".


You may check the correctness, if you want.

-----------------

What is written in the post by @MathLover1, is   A B S U R D,   which I can not comment.

I have no stretch for it . . .

I understand that the person can make a mistake, a typo, an error in calculations.

But in this case, it is far from the common sense boundaries . . .

What every student should understand. looking in this problem, is that 

    - "y" is not a function here.

    - "y" is an independent variable, same as "x", "t", "w" etc.

    - "y" is a dumb variable, which can be replaced by any other symbol.

    - if "y" is used, then the place for the independent variable is just occupied, and there is NO PLACE 
           for other variable symbol to use.

I could expect different things, but not this one from the tutor . . .


Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
∫=
∫ add constant
∫
∫
∫
check

treat , as constants
take the constant out :'=*'

=
=




=
=




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