Work Energy Theorem: Delta K Calculation for Particle Moving in x Direction

[vak3]

A particle moving in the x direction is being acted upon by a net force F(x)=Cx^2, for some constant C. The particle moves from x initial =L to x final=3L. What is Delta K, the change in kinetic energy of the particle during that time?

I tried thih by doing the integral of F(x), replacing x with 2L (because final-initial, 3L-L). I got the answer 2/3 CL^3, and its telling me I am off by a multiplicative factor. Is this because I did the integral wrong, or am I missing something?

Thanks!

 

[Doc Al]

Not sure what you did or what you mean by "replacing x with 2L". Step 1: Find the anti-derivative. Step 2: Evaluate it over the interval x = L to x = 3L. (Evaluate for x = 3L and for x = L and subtract.)