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.

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?

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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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