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Calculus

Numerical Approximation of Integrals

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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