Midpoint Rule Calculator for a Table

For the given table of values, the calculator will approximate the integral using the midpoint rule, with steps shown.

Related calculator: Midpoint Rule Calculator for a Function

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.

Your Input

Approximate the integral $$$\int\limits_{-4}^{4} f{\left(x \right)}\, dx$$$ with the midpoint rule using the table below:

$$$x$$$$$$-4$$$$$$-2$$$$$$0$$$$$$2$$$$$$4$$$
$$$f{\left(x \right)}$$$$$$1$$$$$$2$$$$$$7$$$$$$5$$$$$$3$$$

Solution

The midpoint rule approximates the integral using midpoints: $$$\int\limits_{a}^{b} f{\left(x \right)}\, dx\approx \sum_{i=1}^{\frac{n - 1}{2}} \left(x_{2i+1} - x_{2i-1}\right) f{\left(\frac{x_{2i-1} + x_{2i+1}}{2} \right)}$$$, where $$$n$$$ is the number of points.

$$$\int\limits_{-4}^{4} f{\left(x \right)}\, dx\approx \left(0 - \left(-4\right)\right) f{\left(\frac{0 - 4}{2} \right)} + \left(4 - 0\right) f{\left(\frac{4 + 0}{2} \right)}$$$

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

Therefore, $$$\int\limits_{-4}^{4} f{\left(x \right)}\, dx\approx \left(0 - \left(-4\right)\right) 2 + \left(4 - 0\right) 5 = 28$$$.

Answer

$$$\int\limits_{-4}^{4} f{\left(x \right)}\, dx\approx 28$$$A

If you like the website, please share it anonymously with your friend or teacher by entering his/her email: