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📐 Mathematics  ·  Application of Integrals  ·  JEE

When set up correctly, area is always expressed as a:

Answer: Non-negative quantity.

  • A Negative quantity
  • B Non-negative quantity
  • C Complex number
  • D Function of x only, never a number

Correct answer: B. Non-negative quantity

Explanation: Even though a definite integral can be negative, the area itself is defined as a non-negative quantity, so absolute values are taken where needed.

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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