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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