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📐 Mathematics  ·  Application of Integrals  ·  JEE

The area bounded by y = x³, the x-axis and the lines x = 0 and x = 2 is:

Answer: 4.

  • A 2
  • B 4
  • C 8
  • D 16

Correct answer: B. 4

Explanation: ∫₀² x³ dx = 16/4 = 4.

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 →