Right Endpoint Approximation Calculator for a Table

Approximate an integral (given by a table of values) using the right endpoints step by step

For the given table of values, the calculator will approximate the integral using the right endpoints (the right Riemann sum), with steps shown.

Number of points:

Points:

$$$x$$$
$$$f{\left(x \right)}$$$

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Your Input

Approximate the integral $$$\int\limits_{-5}^{2} f{\left(x \right)}\, dx$$$ with the right endpoint approximation using the table below:

$$$x$$$	$$$-5$$$	$$$-2$$$	$$$0$$$	$$$1$$$	$$$2$$$
$$$f{\left(x \right)}$$$	$$$2$$$	$$$1$$$	$$$5$$$	$$$-2$$$	$$$4$$$

Solution

The right Riemann sum approximates the integral using right endpoints: $$$\int\limits_{a}^{b} f{\left(x \right)}\, dx\approx \sum_{i=1}^{n - 1} \left(x_{i+1} - x_{i}\right) f{\left(x_{i+1} \right)}$$$, where $$$n$$$ is the number of points.

Therefore, $$$\int\limits_{-5}^{2} f{\left(x \right)}\, dx\approx \left(-2 - \left(-5\right)\right) 1 + \left(0 - \left(-2\right)\right) 5 + \left(1 - 0\right) \left(-2\right) + \left(2 - 1\right) 4 = 15.$$$

Answer

$$$\int\limits_{-5}^{2} f{\left(x \right)}\, dx\approx 15$$$A