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📐 Mathematics  ·  Integrals  ·  JEE

Evaluate definite integral: integral from 0 to 1 of x dx

Answer: 1/2.

  • A 0
  • B 1/2
  • C 1
  • D 2

Correct answer: B. 1/2

Explanation: Integral of x = x²/2 + C. Evaluate from 0 to 1: [1²/2] - [0²/2] = 1/2 - 0 = 1/2.

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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