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# Numerical Approximation of Integrals

Whether you want to program a calculator or just approximation an integral on paper, break out some numerical approximation tools like Simpson's Rule and the Trapezoid Rule.

# Riemann Sums and Definite Integrals

Find the approximate value of $$\displaystyle{\int_0^{2} 7x^{2}dx}$$ using a right Riemann sum by dividing the interval into $$4$$ pieces.

Which of the following represents the approximation of $$\displaystyle{\int_{0}^{4}x^{5}dx}$$ using a left Riemann sum?

Find the approximate value of $$\displaystyle{\int_0^1 (6x^2+2)dx}$$ using a right Riemann sum, by dividing the interval into $$7$$ parts.

The following is Alex's approximation of an integration by using a right Riemann sum: $\frac{9}{5}\cdot\left(\left(\frac{3}{5}\right)^{7}+\left(\frac{6}{5}\right)^{7}+\left(\frac{9}{5}\right)^{7}+\left(\frac{12}{5}\right)^{7}+\left(\frac{15}{5}\right)^{7}\right).$ Which of the following integrals is Alex approximating?

What is the Riemann sum of the function $$f(x)= x^3-6x$$ is in the interval $$[0, 6]$$, if we divide it into 3 equal parts and use the midpoint of each interval?

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