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📐 Mathematics  ·  Integrals  ·  JEE

Evaluate: integral from 0 to 1 of eˣ dx

Answer: e-1.

  • A 1
  • B e
  • C e-1
  • D e+1

Correct answer: C. e-1

Explanation: [eˣ] from 0 to 1 = e¹ - e⁰ = e - 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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