Question

The force applied against a moving object travelling on a linear path is given by `F(x)= 2x^3+6x`. How much work would it take to move the object over `x in [2, 3]`?

Answer 1

`W=47.5J`

Explanation:

Work, is an integral of force over distance, that is
`W=\intF(x)dx`

Here, `F(x)=2x^3+6x`
So, integrating `F(x)` with respect to `x` from `2` to `3`,
`int_2^3F(x)dx=\int_2^3(2x^3+6x)dx=(\frac{2x^4}{4}+\frac{6x^2}{2})|_2^3=\frac{3^4-2^4}{2}+3(3^2-2^2)`

Solving the above equation gives you the answer provided above.