A question about Intergration (1 Viewer)

[Volarath]

Consider the following:

dt / dx = 1 / 8x²
t = 1 / 8 x INTERGRAL {x^-2dx}
= 1 / 8 x (-x^-1 + C)

Now, is the next step

= - 1 / 8x + C / 8 OR -1 / 8x + C

I'm trying to find t in terms of x. At t = 1, v = 3.
The two different steps give two very different answers :/
Which step is the correct one?

 

[Trev]

The first one.

 

[word.]

the second one, leave the constant alone.

int(ax^n)
= [ax^(n+1)]/(n+1) + C , (for integers n != -1)

well it doesn't actually matter,
if you wish to take the first approach you'll have to be consistent about it,

eg integrate 2x
int(2x) = 2*int(x) = 2((x^2)/2 + C) = x^2 + 2C

 

[insert-username]

The first one. As a general rule of thumb, leave C by itself - don't multiply it by stuff you've taken out. In other words, when you integrate, you don't know what the value of C is, so there isn't any need to multiply it since your result will still be some constant which you don't know. Leave it as C.


I_F