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प्रश्न
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.
संख्यात्मक
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उत्तर
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.
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