Question

The force applied against a moving object travelling on a linear path is given by `F(x)=x+2e^x`. How much work would it take to move the object over `x in [2, 3]`?

Answer 1

I found: `27.9J`

Explanation:

Here you have a variable force so we need to use the integral form of the work as:
`W=int_(x_1)^(x_2)F(x)dx`
in your case:
`W=int_2^3(x+2e^x)dx=`
`=x^2/2+2e^x` evaluated between `x=2` and `x=3`
`=(3^2/2+2e^3)-(2^2/2+2e^2)=27.9J`