Homework Answer Key Possibly Incorrect - Physics/Calculus

[tfordman]

Edit: Please see first reply!

Hey all! I'm doing my physics homework (online) and think I may have run into an issue. I suspect that the key by which the homework engine grades the problems may be incorrect.

Now - I realize this is the Calculus+ section of the Homework section, but my question pertains principally to the calculus aspect of the question; thus I am posting here. This is also my first post, so please do correct me if I'm wrong in deciding to post my question here! I've also never heard of, much less used, LaTeX before, so forgive me if the formatting looks ugly. It certainly looks a lot better than a question littered with ^, /, and the like, though.

1. Homework Statement
Now, this is a pretty simple problem in which you are to find the potential energy given the force vector. To do this you must integrate the force vector to obtain the potential energy (as PE = U = $\int F_x dx$).

The force vector/integrand in this case is $-A x + B x^6$.

It's also stated that U = 0 at x = 0. It should also be noted that A and B are constants.

Homework Equations

I'm not sure there are any relevant equations which are worth writing out here (i.e. rules of integration); however, I could possibly be missing a rather basic integration rule here (or rather, simply forgot one).

The Attempt at a Solution

My first course of action was to split the integral into two separate integrals:
$\int -A x + B x^6 dx$ = $\int -A x dx$ + $\int B x^6 dx$

Next, I brought the constants out from the integrals:
$-A \int x dx$ + $B \int x^6 dx$

Integrating as usual, I found the answer to be:

U(x) = $\frac{-A x^2} {2}$ + $\frac{B x^7} {7}$ $+C$

Since U = 0 when x = 0 as stated, C is easily calculated to = 0 and thus can be omitted from the final answer.
However, the homework engine will not accept this as a valid solution! Instead, it accepts only:

U(x) = $\frac {A x^2} {2}$ - $\frac {B x^7} {7}$

Have I made a fundamental error in my integration? I feel like accusing the online homework key of being wrong is akin to scholastic blasphemy, but I want to know if I am missing something in my own knowledge.

Thank you for taking the time to read my question!
-T

 

[tfordman]

Wait, I have discovered my error. It's not with the calculus; rather, I simply forgot that F_x = $-\frac{dU} {dx}$. I forgot to apply the minus sign after integrating! I'm not sure how to delete a thread so I figured I'd post here. I suppose this belongs in the Physics section after all!

 

[Bystander]

Good catch --- .