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📐 Mathematics  ·  Integrals  ·  JEE

The area bounded by y = x², x-axis, x = 0 to x = 3:

Answer: 9.

  • A 6
  • B 8
  • C 9
  • D 27

Correct answer: C. 9

Explanation: Area = integral from 0 to 3 of x² dx = [x³/3] = 27/3 - 0 = 9.

xyabArea = integral of f(x) dxRectangles approximate the area (Riemann sum)

The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.

Concept context

Indefinite and definite integrals, areas under curves

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