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### Section 7.10 : 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. $$\displaystyle \int_{{ - 2}}^{4}{{\sin \left( {{x^2} + 2} \right)\,dx}}$$ using $$n = 6$$
2. $$\displaystyle \int_{0}^{4}{{\sqrt{{{x^4} + 6}}\,dx}}$$ using $$n = 6$$
3. $$\displaystyle \int_{1}^{5}{{{{\bf{e}}^{\cos \left( x \right)}}\,dx}}$$ using $$n = 8$$
4. $$\displaystyle \int_{3}^{5}{{\frac{1}{{1 - \ln \left( x \right)}}\,dx}}$$ using $$n = 6$$
5. $$\displaystyle \int_{{ - 3}}^{1}{{\sin \left( x \right)\cos \left( {{x^2}} \right)\,dx}}$$ using $$n = 8$$