Calculus

# 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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