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The integral $\int_{x_{1}}^{x_{2}}x^{2}\:dx$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and $J$ is the approximate value obtained using the trapezoidal rule, which of the following statement is correct about their relationship?

  1. $J>I$
  2. $J<I$
  3. $J=I$
  4. Insufficient data to determine the relationship
in Numerical Methods recategorized by
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