Right Endpoint Approximation Calculator for a Table

For the given table of values, the calculator will approximate the integral using the left endpoints (the left 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