Learn in the textbookLinear Algebra, Calculus, and Error
DefinitionIn differentiation and integration (微分と積分), differentiation finds the rate of change at a point (the slope of the graph), while integration adds up finely divided pieces to find a total amount (such as an area).
ExplanationFor example, differentiating position with respect to time gives the speed at each instant, and integrating speed over time gives the distance travelled. The branch of mathematics that deals with such changing quantities is called analysis (解析).
AnalogyThe flow rate from a tap corresponds to what differentiation gives, and the amount of water that builds up in the bucket corresponds to what integration gives.
Memory hookDifferentiation looks at the tiny difference between nearby values, while integration, like "integrate" in everyday English, puts the pieces together into a whole.