# 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.

Related calculator: Right Endpoint Approximation Calculator for a Function

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

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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

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