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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
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
- the Midpoint Rule,
- the Trapezoid Rule, and
- Simpson’s Rule.
Use at least 6 decimal places of accuracy for your work.
- \( \displaystyle \int_{{ - 2}}^{4}{{\sin \left( {{x^2} + 2} \right)\,dx}}\) using \(n = 6\)
- \( \displaystyle \int_{0}^{4}{{\sqrt[3]{{{x^4} + 6}}\,dx}}\) using \(n = 6\)
- \( \displaystyle \int_{1}^{5}{{{{\bf{e}}^{\cos \left( x \right)}}\,dx}}\) using \(n = 8\)
- \( \displaystyle \int_{3}^{5}{{\frac{1}{{1 - \ln \left( x \right)}}\,dx}}\) using \(n = 6\)
- \( \displaystyle \int_{{ - 3}}^{1}{{\sin \left( x \right)\cos \left( {{x^2}} \right)\,dx}}\) using \(n = 8\)