Integration of an interaction force to find potential energy

[miyayeah]

Homework Statement

A particle that can move along the x-axis experiences an interaction force Fx=(3x²−5x) N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules.

Homework Equations

I used simple integration rules to solve this problem.

The Attempt at a Solution

∫(3x²−5x) = x³-5/2 x²+C

I put this answer and the feedback said to "check your signs". I was confident that the above was right, so where is my mistake in the sign?

 

[RedDelicious]

You did the integral correctly, but you're missing the physics bit of it.

Is the potential energy really just given by the integral of the force? Try it on Hooke's law.

F = -kx ---> U(x) = -1/2 kx^2? Does this seem right?

The punch here is that, for F = F(x)

$$F(x) = -\frac{dU}{dx}$$

note the minus sign