Terminology repaired — which term is directly named after the calculus operation that accumulates area under a curve (i.e., produces an output proportional to the integral of the input)?

Introduction / Context:
Analog signal-processing blocks often take their names from calculus: circuits that compute time derivatives are called differentiators, while those that accumulate area under an input curve are called integrators. This question focuses on the term whose meaning comes directly from the integral operation in calculus.

Given Data / Assumptions:

• We seek the term explicitly tied to accumulation (area under curve).
• Idealized op-amp models are assumed when thinking of canonical circuits.
• Basic continuous-time linear circuits context.

Concept / Approach:
An integrator produces an output proportional to the time integral of its input: v_out(t) = (1/RC) * ∫ v_in(t) dt for the canonical RC op-amp integrator (constant factors depend on configuration). Conversely, a differentiator outputs a scaled time derivative of the input. Therefore, “integrator” is the term directly derived from the calculus integral.

Step-by-Step Solution:

Verification / Alternative check:
Standard op-amp texts show the inverting integrator with a capacitor in the feedback path and a resistor at the input, yielding v_out proportional to the integral of v_in.

Why Other Options Are Wrong:

• Differentiator: corresponds to the derivative, not the integral.
• Filter: generic term; can be integrative in effect but is not a calculus operation name.
• Voltage-divider: a passive pair of resistors that scales voltage; unrelated to calculus operations.

Common Pitfalls:
Assuming both “differentiator” and “integrator” fit because both come from calculus. The stem was repaired to specify the integral (accumulation) concept to ensure a unique correct choice.

Final Answer:
Integrator.