Question

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]`?

Answer 1

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`