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📐 Mathematics  ·  Application of Integrals  ·  JEE

The definite integral of a function between two limits gives the ___ under the curve:

Answer: area.

  • A area
  • B slope
  • C tangent
  • D derivative

Correct answer: A. area

Explanation: A definite integral evaluates the area bounded by the curve and the x-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.

Read the full Application of Integrals notes →