Question

The force applied against a moving object travelling on a linear path is given by `F(x)=3xe^x`. How much work would it take to move the object over `x in [2, 7]`?

Answer 1

I got: `W=19,717J`

Explanation:

Here you have a variable force (changes with distance `x`) so to evaluate the Work we need to use the integral version as:

`W=int_(x_1)^(x_2)F(x)dx`

or, in your case:

`W=int_2^7(3xe^x)dx=` by parts:

`=3[xe^x-e^x]` between `x=2` and `x=7` gives you:

`W=19,717J`