10) Over a given region, a force (in Newton) varies as F = 3x2 - 2x + 1. In this region an objet
displaced from x1 = 20 cm to x2 = 40 cm by the given force. Calculate the amount of
done
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Answer:
workdone by body =
upper limit = 40
integration sign (3x² - 2x + 1) dx
lower limit = 20
upper limit = 40
= [ (3x³)/(3) - (2x²) /( 2) + x ]
lower limit = 20
upper limit = 40
= [ (x³) - (x²) + x ]
lower limit = 20
= [ (40 ³) - (40 ²) + 40] - [20 ³ - 20² + 20 ]
= [ 64000 - 1600 - 8000+ 400 + 20
= 48000 - 1200 + 20
= 47800 + 20 = 47820
In SI = 47820 x 10^(-2)
= 478.2
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