The force applied against a moving object travelling on a linear path is given by #F(x)= 4x + 4#. How much work would it take to move the object over #x in [ 4 , 7] #?

1 Answer
Oct 17, 2017

Answer:

I got #78J#

Explanation:

In this case you have a variable force #F(x)=4x+4# that depends upon position #x#, so we need to use a small work to evaluate it at each position:

#dW=F(x)dx#

To get the entire amount along your entire displacement we can integrate the above expression to get the total work as:

#W=int_4^7(4x+4)dx#

integrating:

#W=cancel(4)^2x^2/cancel(2)+4x=2x^2+4x# evaluated between #4 and 7#:

#W=(2*7^2+4*7)-(2*4^2+4*4)=78J#