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What is the use of the integrated formulla of work done

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The basic work relationship W=Fd is a case which applies only to constant force along a straight line. In the more general case of a force which changes with distance, ie the variable force (may be because of friction or external force) the work may be calculated using Integrated formula is used.
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Fundamentals, Revision, Numericals and Practice

It is useful if force is variable. If F= f(s) is provided, calculate Integration of F.ds and you will get W.
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Mathmetics tution

It is used to calculate the work done on a body by the resultant external force acting on it
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Integral of f.ds
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-fdx
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Tutor

It gives total work done
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Science Field

work done=integrating of (force dot displacement) limits is to be put from a point to the other point
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US states commoncore, IB, IGCSE, SAT, 18 years of experience in Online tutoring

W= ?f (x) dx . This is when force is changing. Definite integral a to b should be taken.
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If a force is constantly applief work done is product of force and fistance, bot in a varying force over distance covered its integral will give workdone.
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