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Section 1-10 : Approximating Definite Integrals

For each of the following integrals use the given value of n to approximate the value of the definite integral using

  1. the Midpoint Rule,
  2. the Trapezoid Rule, and
  3. Simpson’s Rule.

Use at least 6 decimal places of accuracy for your work.

  1. \( \displaystyle \int_{1}^{7}{{\frac{1}{{{x^3} + 1}}\,dx}}\) using \(n = 6\) Solution
  2. \( \displaystyle \int_{{ - 1}}^{2}{{\sqrt {{{\bf{e}}^{ - \,{x^{\,2}}}} + 1} \,dx}}\) using \(n = 6\) Solution
  3. \( \displaystyle \int_{0}^{4}{{\cos \left( {1 + \sqrt x } \right)\,dx}}\) using \(n = 8\) Solution