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📐 Mathematics  ·  Application of Integrals  ·  JEE

If a curve lies below the x-axis, its definite integral gives a ___ value:

Answer: negative.

  • A negative
  • B positive
  • C zero
  • D complex

Correct answer: A. negative

Explanation: Below the axis the signed area is negative, so the raw integral is negative.

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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