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📐 Mathematics  ·  Integrals  ·  JEE

The value of the definite integral of lnx from 1 to e is:

Answer: 1.

  • A 0
  • B 1
  • C e
  • D e − 1

Correct answer: B. 1

Explanation: ∫ lnx dx = x lnx − x; from 1 to e this is (e − e) − (0 − 1) = 1.

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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