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.

##### The formula used is as follows:

#### 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.

## Types of Integration Approximation calculator

- Midpoint Rule calculator
- Trapezoidal Rule calculator
- Left Rectangular Approximation Calculator
- Right Rectangular Approximation Calculator
- Approximation Calculator