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📐 Mathematics  ·  Application of Integrals  ·  JEE

Physical area is always taken to be a ___ quantity:

Answer: a strictly non-negative value.

  • A a strictly non-negative value
  • B a strictly negative value
  • C an always-zero value
  • D a possibly complex value

Correct answer: A. a strictly non-negative value

Explanation: Area is measured as a non-negative amount, so we use absolute values where a curve dips below the axis.

Area Under a Curve = Definite Integralxyx=ax=bArea = ∫ₐᵇ f(x)dx

The definite integral ∫ₐᵇf(x)dx computes the exact area of the shaded region bounded by the curve, the x-axis, and the vertical lines x=a and x=b - the same idea behind the Riemann sum, but evaluated exactly rather than approximated by rectangles.

Concept context

Using definite integrals to compute the area under a curve, the area between two curves, and the areas enclosed by standard curves like circles, parabolas, and ellipses.

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