Right Endpoint Approximation Calculator for a Table
For the given table of values, the calculator will approximate the integral using left endpoints (the left Riemann sum), with steps shown.
Related calculator: Right Endpoint Approximation Calculator for a Function
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 left Riemann sum approximates the integral using left 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