﻿ Integral Approximation Calculator - MathAuditor

# Integral Approximation Calculator

Integral approximation calculators are used to simplify calculations for us by directly calculating values of the definite integrals without much effort and time saved. They are readily available online, and they require no purchasing. They have a user- friendly interface. These are taught to students in first-year calculus.

## What are the integration approximations?

In basic mathematics, integration is a method of finding the area under the curve. It is done by adding consecutive slices of the field together. It is amongst the most feasible ways to find the area under graph but at times, finding the area of the curve seems unfeasible because of complex calculations. Humans are prone to making errors, which would lead to misleading results. Due to this reason, the integration of approximations methods is used. Integration approximations calculator help in evaluating such integrals efficiently with the use of approximations.

## What are integral approximation calculators?

Humans are prone to committing errors. Errors can be determined while calculating large values. To help this, integral approximation calculators were developed. There are several types of integral approximation calculators as follows:

#### 1. Midpoint Rule Calculator

An intuitive method of finding the area of a curve by approximating that area with a series of rectangles between the intervals. Midpoint Rule calculator is an online integral approximation calculator used for approximating a definite integral using the midpoint rule.

#### 2. Trapezoidal Rule Calculator

The trapezoidal rule is a technique that is utilized to approximate values of definite integrals. The key to implementing trapezoidal rule is assuming the area of the integral, i.e. the area under the graph to be a trapezoid. Assuming the area under the graph to be a trapezoid, the approximate value of the integral can be calculated using the following formula:

##### The formula used is as follows:
For a more accurate approximation, partitioning of the integral sum can be done and then the trapezoidal rule can be applied to each subinterval and finally summed to obtain the result.

#### 3. Simpson's Rule Calculator

Simpson’s Rule Calculator is used to calculate the approximate values of definite integrals involving parabolas. It is used to calculate results of the area above or beneath the parabola.

##### The formula used is as follows:
This can be further simplified to Simpson’s 1/3rd Rule

###### Left Rectangle Approximation Calculator

The left rectangular integral approximation calculator approximates the definite integrals with the help of Riemann sums using left endpoints. In mathematics, Riemann sums are used to approximate areas under graphs using finite sums.

###### Right Rectangular Approximation Calculator

The right rectangular integral approximation calculator approximates the definite integrals with the help of Riemann sums using right endpoints. In mathematics, Riemann sums are used to approximate areas under graphs using finite sums.