Use a right Riemann sum with $4$ sub-intervals to estimate:

$\displaystyle\int_0^4 (x^4 + 5)dx$

Use a left Riemann sum with $3$ sub-intervals to estimate:

$\displaystyle\int_0^{\frac{3π}{2}} \cos(x)dx$

Use a Midpoint Riemann sum with $2$ sub-intervals to estimate:

$\displaystyle\int_0^4 (x^2 + 1)dx$

Use the following table to calculate a right Riemann sum on the interval $[0, 4],$ $ (Δx = 1)$.

Use the following table to calculate a left Riemann sum on the interval $[0, 4],$ $ (Δx = 1)$.

Use the following table to calculate a midpoint Riemann sum on the interval $[0, 6],$ $n = 3$.

Use a trapezoidal sum to approximate the area under the curve for the function $f(x) = 3x^2$ on the interval $[0, 6]$ with $n = 6$.

Use a trapezoidal sum to approximate the area under the curve for the function $f(x) = x^5 − x^2$ on the interval $[0, 4]$ with $n = 4$.

Find the average value of the function $f(x) = x^3 + 2x^2$ on the interval $[0, 5]$.

Find the average value of the function $f(x) = e^{2x} + 5$ on the interval $[0, 3]$.

Find the average value of the function $f(x) = \sin⁡(x)\cos⁡(x)$ on the interval $\left[0, \frac{π}{2}\right]$.

Find the average value of the function $f(x) = \tan⁡(x)$ on the interval $\left[ 0, \dfrac{π}{3}\right]$.