Integrating to find potential energy from force

[Sneakatone]

I took the integral of the equation but its wrong, the program does not have a fraction input to put 1/4 properly. I ended up with -x^-1/4(x^4).
For part b I plugged in 4.5 and turned the number positive to get the answer.
Did I do something wrong for part a?

 

[voko]

That you had to turn the number positive should ring a bell.

 

[Sneakatone]

If I plugged in 4.5 into the antiderivative then it would be -122 and that's not correct

 

[voko]

What is the relationship between F and U?

 

[Sneakatone]

F=U/x

 

[voko]

You need a review on that.

 

[Sneakatone]

force is the derivative of potential energy which means the antiderivative of force is potential energy

 

[voko]

That's not exactly correct. Why do you think you had to massage the sign to make the ends meet?

 

[Sneakatone]

is it because U(x)=0

 

[voko]

Stop guessing. Get your textbook, and find out how potential energy and force are related.

 

[Sneakatone]

F=-dU/dx
but when I put in x^2+1/4x^4 or -(-x^2-1/4^4) it is still wrong

 

[voko]

For F(x) = -2x - x^3, U(x) = x^2 + (x^4)/4 is correct. I do not know why it is not accepted. Perhaps there is some particular way you should enter it.

 

[Sneakatone]

when I input that it says ''this is not a definite integral''