1. ## Work-Related Integration Problem

[SOLVED]

I've been having trouble with this one. Help appreciated

A carpet which is 7 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is

F(x)=900/(x+2)^3 Newtons.

How much work is done unrolling the entire carpet? Your answer must include the correct units.

2. Originally Posted by Kimmy2
I've been having trouble with this one. Help appreciated

A carpet which is 7 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is

F(x)=900/(x+2)^3 Newtons.

How much work is done unrolling the entire carpet? Your answer must include the correct units.
$\displaystyle W = \int_{x_1}^{x_2} F(x) \, dx$

$\displaystyle W = \int_0^7 \frac{900}{(x+2)^3} \, dx$

units of work are Newton-meters = Joules

3. I tried integrating using that method. I got -1/162.
According to the website I get my homework from, it recorded that answer as incorrect. Did I integrate incorrectly?

Am I supposed to use f(x)=kx, W=Fd, F=ma, somehow?

4. Originally Posted by Kimmy2
I tried integrating using that method. I got -1/162.
According to the website I get my homework from, it recorded that answer as incorrect. Did I integrate incorrectly?

Am I supposed to use f(x)=kx, W=Fd, F=ma, somehow?
I can tell you that the answer you have for the integral is incorrect. What did you get for your anti-derivative?

5. I got (-450/x^2+4x+4).

6. Originally Posted by Kimmy2
I got (-450/x^2+4x+4).
you need to integrate

$\displaystyle \int_{0}^{7}\frac{900}{(x+2)^3}dx$

Try a u-sub with $\displaystyle u=x+2 \implies du=dx$

See if you can get it from here.

7. Originally Posted by Kimmy2
I got (-450/x^2+4x+4).
$\displaystyle \left[-\frac{450}{(x+2)^2}\right]_0^7 = \frac{1925}{18}$

8. Woah. Thanks, Skeeter! That answer was correct. I wonder what I did wrong

9. Originally Posted by Kimmy2
Woah. Thanks, Skeeter! That answer was correct. I wonder what I did wrong
I don't know ... you didn't show your work.