Reverse of differentiation. The constant C accounts for any constant term lost during differentiation.
Physics — Distance from velocity: s = ∫v dt.
Economics — Total cost from marginal cost: TC = ∫MC dq.
Engineering — Area under stress-strain curve = energy absorbed.
Biology — Total population from growth rate.
Finance — Present value from cash flow rate.
Chemistry — Total amount from reaction rate.
Statistics — CDF from PDF: F(x) = ∫f(x)dx.
Electrical — Charge from current: Q = ∫I dt.
Mechanics — Work from force: W = ∫F dx.
Hydrology — Total flow from flow rate.
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