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, 3 ]`?

Answer 1

`W=6.e^3-3.e^2`

Explanation:

`W= int _2^3 F(x). d x=int _2^3 3.x.e^x.d x=3int_2^3 x.e^x.d x`
`W=3.[e^x(x-1)]_2^3=3([e^3(3-1)]-[e^2(2-1)])`
`W=3.(2.e^3-e^2)`
`W=6.e^3-3.e^2`