Question

Variation of a force in a certain region is given by F = 6x² – 4x – 8. It displaces an object from x = 1 m to x = 2 m in this region. Calculate the amount of work done.

Answer 1

W = \[\int\limits_{x = 1}^{x = 2} (6x^2 - 4x - 8)\]

∴ W = \[\int\limits_{x = 1}^{x = 2}6x^2 dx - \int\limits_{x = 1}^{x = 2} 4x^2 dx - \int\limits_{x=1}^{x = 2}8 dx\]

`= [(6"x"^3)/(3)]_1^2 - [(4"x"^2)/2]_1^2 - ["8x"]_1^2`

= (16 − 2) − (8 − 2) − (16 − 8) = 0

The work done is zero.