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    Negative and positive work - Question

    I accelerate a mass upward by 2G (2×force of gravity) over some change in height Δh_{1}, then I apply only \frac{1}{2}G over some other change in height Δh_{2}. If, over Δh_{2}, the mass still moving upward (but accelerating downwards), am I doing positive work over Δh_{2} even though the mass...
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    Elementary Integration - First Principles?

    Is there an first-principles equation for integration that can be explicitly solved like that for differentiation? - I'm trying to understand Integration intuitively. Thanks heaps. I've tried to piece together one but can't quite solve it (for simple functions like f = x). Things cancel and...