Numerical Approximations to Definite Integrals

Practice Questions

AP Calculus BC › Numerical Approximations to Definite Integrals

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$\begin{align*}&\text{Using the method of left point Riemann sums approximate the integral:}\&\int_{0}^{12}(11sin(20sin(x)))dx\&\text{Using }3\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Calculate the Riemann sums integral approximation of :}\&\int_{-2}^{11.6}(\frac{18}{3^{(4tan(4x))}})dx\&\text{Using left points over }4\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Using the method of left point Riemann sums approximate the integral:}\&\int_{0}^{12}(11sin(20sin(x)))dx\&\text{Using }3\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Calculate the Riemann sums integral approximation of :}\&\int_{-2}^{11.6}(\frac{18}{3^{(4tan(4x))}})dx\&\text{Using left points over }4\text{ intervals.}\end{align*}$

$\begin{align*}&\text{Calculate the right-side Riemann sums integral approximation of :}\&\int_{-1}^{15}(3x + 5sin(2e^{(2x)}))dx\&\text{Using points over }4\text{ intervals.}\end{align*}$

Approximate

$\int_{1}^{2} e ^{x^{2}} \mathrm{d}x$

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

$\begin{align*}&\text{Using the method of left point Riemann sums approximate the integral:}\&\int_{0}^{3}(-16sin(2x^{2}))dx\&\text{Using }3\text{ intervals.}\end{align*}$