Question

The force applied against a moving object travelling on a linear path is given by `F(x)=2x+xe^x`. How much work would it take to move the object over `x in [1,2 ]`?

Answer 1

`W= 3+e^2` Joule

Explanation:

`F(x) = 2x+xe^x`

As we know,

`dW= vec F * vec(dx)`

Integrating both sides

`W= int_1^2(2x+xe^x)dx`

`W= [x^2]_1^2+int_1^2xe^xdx`

Applying by-parts by ILATE rule,

`W= [x^2]_1^2+[xe^x]_1^2-int_1^2e^xdx`

`W= [x^2]_1^2+[xe^x]_1^2-[e^x]_1^2`

`W= 4-1+2e^2-e-e^2+e` Joule

`W= 3+e^2` Joule