Help with a work problem(spring)

[mathnoobie]

Homework Statement

A force of 4 lbs is needed to stretch a 10-in. spring 1 inch beyond its natural length.
Find the work done in stretching the same spring from its natural length to a length of 15 inches.

Homework Equations

f=kd
W=∫(kx)dx

The Attempt at a Solution

So I know that a force of 4lbs is required to stretch a spring 1inch.
so 4=1K
K=4
I plug K into my work equation and i get
∫(4x)dx
I integrate it and get 2x^2 from 0 to 15/12(converting to feet)
I plug in my limits of integration and I get 3.125ft-lbs

The solution says ~4.167 ft-lbs.

I have no idea where I went wrong.

 

[Doc Al]

15 inches is the total length of the stretched spring. Don't convert units until after you've evaluated the integral.

 

[mathnoobie]

15 inches is the total length of the stretched spring. Don't convert units until after you've evaluated the integral.

Ah, ok. I retried the integral going from 0 to 5
I also noticed one mistake I made. I converted my limits of integration to foot in my integral but when I was solving for K, I didn't convert it.
So it would be 4=k/12
k=48

Doing this did indeed give me the correct answer. Thank you!