Riemann sums (left, right, and midpoint evaluation points)

Practice Questions

AP Calculus AB › Riemann sums (left, right, and midpoint evaluation points)

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Estimate the integral of from 0 to 3 using left-Riemann sum and 6 rectangles. Use $\Delta x=0.5$

Let $f(x) = \frac{1}{7}x^{7} - \frac{6}{5} x^{5} + \frac{5}{3}x^{3} - 30x$ .

A relative maximum of the graph of can be located at:

$\begin{align*}&\text{The function }f(x)\text{ has the following values on the interval }x=[-8,2]:\&f(-8)=2\&f(-6)=-1\&f(-4)=16\&f(-2)=12\&f(0)=10\&f(2)=-18\&\text{Approximate the integral of }f(x)\text{ on this interval using left Riemann sums.}\end{align*}$

$\begin{align*}&f(-10)=-19\&f(-3)=7\&f(4)=4\&f(11)=1\&\text{Approximate, using a left Riemann sum, }\int_{-10}^{11}f(x)\end{align*}$

$\begin{align*}&\text{Approximate }\int_{5}^{13}f(x)\&\text{Using a left Riemann sum, if }f(x)\text{ has the values:}\&f(5)=-7\&f(7)=-8\&f(9)=-18\&f(11)=-8\&f(13)=-19\end{align*}$

$\begin{align*}&\text{The function }f(x)\text{ has the following values on the interval }x=[1,11]:\&f(1)=10\&f(3)=3\&f(5)=-13\&f(7)=4\&f(9)=-8\&f(11)=-15\&\text{Approximate the integral of }f(x)\text{ on this interval using right Riemann sums.}\end{align*}$

$\begin{align*}&\text{Approximate }\int_{-6}^{39}f(x)\&\text{Using a right Riemann sum, if }f(x)\text{ has the values:}\&f(-6)=-4\&f(3)=-1\&f(12)=11\&f(21)=13\&f(30)=-16\&f(39)=-13\end{align*}$

$\begin{align*}&\text{Approximate }\int_{5}^{23}f(x)\&\text{Using a left Riemann sum, if }f(x)\text{ has the values:}\&f(5)=-3\&f(11)=8\&f(17)=11\&f(23)=-3\end{align*}$