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📐 Mathematics  ·  Integrals  ·  JEE

Evaluate: integral from 1 to 2 of x² dx

Answer: 7/3.

  • A 7/3
  • B 8/3
  • C 7/2
  • D 3

Correct answer: A. 7/3

Explanation: Integral of x² = x³/3. Evaluate: [8/3] - [1/3] = 7/3.

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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