Riemann Sum: Midpoint Evaluation

Practice Questions

AP Calculus BC › Riemann Sum: Midpoint Evaluation

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$\begin{align*}&\text{Using the method of midpoint Riemann sums approximate the integral:}\&\int_{-2}^{4.6}(9tan(9tan(6x)))dx\&\text{Using }3\text{ intervals.}\end{align*}$

Approximate

$\int_{0}^{\frac{\pi}{2}} x^{2} \cos x ; \mathrm {d}x$

using the midpoint rule with . Round your answer to three decimal places.

Approximate

$\int_{1}^{2} x^{2} \ln x ; \mathrm {d}x$

using the midpoint rule with . Round your answer to three decimal places.

$\begin{align*}&\text{Using the method of midpoint Riemann sums approximate the integral:}\&\int_{1}^{9}(19cos(2x^{2}))dx\&\text{Using }4\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Using }4\text{ intervals, and the method of midpoint Riemann sums approximate the integral:}\&\int_{1}^{12.6}(-9sin(18e^{(3x)}))dx\end{align*}$

$\begin{align*}&\text{Using the method of midpoint Riemann sums approximate the integral:}\&\int_{4}^{9.4}(-15sin(x^{2}))dx\&\text{Using }3\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Using the method of midpoint Riemann sums approximate the integral:}\&\int_{5}^{21}(-16cos(sin(6x)))dx\&\text{Using }4\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Using }3\text{ intervals, and the method of midpoint Riemann sums approximate the integral:}\&\int_{2}^{14.6}(16cos(20e^{(3x)}))dx\end{align*}$

$\begin{align*}&\text{Using }3\text{ intervals, and the method of midpoint Riemann sums approximate the integral:}\&\int_{-3}^{9.9}(\frac{13}{3^{(5cos(3x))}})dx\end{align*}$

$\begin{align*}&\text{Calculate the Riemann sums integral approximation of :}\&\int_{-4}^{14.4}(-20sin(13tan(2x)))dx\&\text{Using midpoints over }4\text{ intervals.}\end{align*}$

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