what’s the rate at which paint is being laid down when the roller is at x? To answer that, think about what happens in the next infinitesimal interval of time. The roller rolls to the right through some infinitesimal distance dx. Meanwhile, as it traverses that tiny distance, it keeps its length y in the vertical direction almost perfectly constant, since there’s almost no time for it to change its length during the infinitesimally brief roll (a fine point that we’ll discuss in the next chapter). During that brief interval, it paints what is essentially a tall, thin rectangle of height y,
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