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📐 Mathematics  ·  Integrals  ·  JEE

The value of the definite integral of x³·e<sup>x²</sup> from −1 to 1 is:

Answer: 0.

  • A 0
  • B 2e
  • C 1
  • D e − 1/e

Correct answer: A. 0

Explanation: The integrand is an odd function on a symmetric interval, so the integral is 0.

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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