Expert: Ahmed Salami - 1/20/2010

Question
I have attempted this problem multiple times and cannot receive the correct answer.  I was wondering if you would be able to help me understand how to do this problem because i thought it would only be the integral from 0 to 8 of the function.  But i was wrong. Thank you so much for your help, hope you have better luck than me!

PROBLEM:  A carpet which is 8 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is

F(x)=700/((x+2)^5) Newtons
How much work is done unrolling the entire carpet? Your answer must include the correct units.

Answer
Hi Krista,
Work done is ∫F(x) dx  from x = 0 to 8
W = ∫[700/(x+2)^5] dx
 = ∫[700(x+2)^-5] dx
 = [700(x+2)^-4]/-4
 = [-175/(x+2)^4]    from x = 0 to 8
 = [-175/(8+2)^4] - [-175/(0+2)^4]
 = [-175/(10)^4] - [-175/(2)^4]
 = [-175/10000] - [-175/16]
 = 10.92 Joules

Maybe if you showed me what you did i could have just pointed out your error.

Regards