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📐 Mathematics  ·  Application of Integrals  ·  JEE

The area between an upper curve f(x) and a lower curve g(x) is ∫[f(x) − g(x)] dx taken over their:

Answer: points of intersection.

  • A points of intersection
  • B their entire domain
  • C their whole range
  • D their common tangent

Correct answer: A. points of intersection

Explanation: The limits are the x-values where the two curves intersect.

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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