## Introduction to the Simpson's Rule Calculator

The Simpson's rule integral Calculator is an online freely-available tool used to determine the area. The **simpson rule online calculator** for the area, for the approximation of the definite integral by determining the area under a parabola. This calculator also works for the quadratic equation.

This Simpson's calculator is easy to use and gives accurate results. Simpson's rule is more accurate than the trapezoidal rule calculator in giving more accurate solutions to the definite integral functions.

## What is Simpsons Rule Calculator?

The **simpson's rule formula calculator** helps to evaluate the parabola online. The curve is considered as a whole and the partitioning of the parabola. Simpson's rule error calculator is for the approximation of definite integrals for the quadratic functions instead of calculating the area of rectangles.

Simpson's rule volume calculator is the best tool for evaluating or approximating the area under the curve as a whole. There are many other way to approximate the integral like riemann sum integration calculator, but simpson rule online calculator is one of the best tool for such type of complex calculations.

## Formula Used by Simpson's Rule Formula Calculator

The Simpson's integral rule calculator with steps calculates the area of a parabola by step-by-step instructions. Calculation of calculus are complex sometimes, but with the help of proper concept and formula it become quite easier. The **Simpson's Calculator** uses the following formula to solve the problems:

$$ \int_a^b f(x) \; x' \;=\; \frac{Δx}{3} (f(x_0)+4f(x_1)+2f(x_2)+...+4f(x_{n-1})+f(x_n)) $$

Where,

Δx = (b-a)/n

x_{i} = a + iΔx

Let's Understand how our simpson's rule calculator table uses this formula to solve the complex integration problems in a seconds.

## How to Estimate Integral with Simpson's Rule?

Following is the detailed step by step solution of process of estimating the integral with the help of simspon's rule. The example is as follow:

**Example:** Use Simspons's rule with n = 4, to estimate the integral:

$$ \int_1^2 \;=\; \frac{dx}{x} $$

**Solution:**

Subintervals will:

$$ \frac{b-a}{n} \;=\; \frac{2-1}{4} \;=\; \frac{1}{4} $$ $$ So, x_0 \;=\; 0 \;,\; x_1 \;=\; 1\frac{1}{4} \;,\; x_2 \;=\; 1\frac{1}{2} \;,\; x_3 \;=\; 1\frac{3}{4} \;,\; x_4 \;=\; 2 $$ $$ f(x_0) \;=\; \frac{1}{1} \;=\; 1 $$ $$ f(x_1) \;=\; \frac{1}{1\frac{1}{4}} \;=\; \frac{4}{5} $$ $$ f(x_2) \;=\; \frac{1}{1\frac{1}{2}} \;=\; \frac{2}{3} $$ $$ f(x_3) \;=\; \frac{1}{1\frac{3}{4}} \;=\; \frac{4}{7} $$ $$ f(x_4) \;=\; \frac{1}{2} $$

Using the formula of **simpsons rule calculator**,

$$ \int_a^b f(x) \; x' \;=\; \frac{Δx}{3} (y_0 + 4y_1 + 2y_2 +...+ 2y_{n-2} + 4y_{n-1} + y_n) $$ $$ \int_1^2 \frac{dx}{x} \; x' \;=\; \frac{1}{12} \left( 1 + (4)\frac{4}{5} + 2 \frac{2}{3} + 4 \frac{4}{7} + \frac{1}{2} \right) $$ $$ \int_1^2 \frac{dx}{x} \; x' \;=\; \frac{1}{12} \left( 1 + \frac{16}{5} + \frac{4}{3} + \frac{16}{7} + \frac{1}{2} \right) $$ $$ \int_1^2 \frac{dx}{x} \; x' \;=\; \frac{1}{12} + \frac{4}{15} + \frac{1}{9} + \frac{4}{21} + \frac{1}{24} $$ $$ \int_1^2 \frac{dx}{x} \; x' \;=\; 0.693253968 $$

So, in this way our tool calculate perform calculation to provide you the results in a blink of your eye.

## How does Simpson's Method Calculator Works?

By following the below steps for the Simpsons rule formula calculator, you can get the solution to your given problems:

- Enter the function in the "EQUATION BOX".
- Put the values of upper and lower bound as we put in definite integral solver.
- Select the size of "intervals" to esimate the area.
- Now, Hit the "CALCULATE" button for processing the results.

**Output:**

The simpsons rule calculator will show:

- The estimation of integral with the help of simpsons method rule.
- Symbolic form of simpson's rule.
- Plot of the area occupied by our function.
- Comparision of exact inegral area vs approximation by this method.

## How to Get This Simpson's Rule Error Calculator Online?

To find the Simpson's rule integral calculator for calculating the area under the curve as a whole. By using the following steps, you can get the Simpson's Rule Online calculator:

- First of all, open your default browser's home screen.
- Enter the calculator keywords
**Simpson's rule calculator**or simpson rule calculator with steps in the search bar. - Now, wait for your search results to appear on your screen.
- Now select the Integral Calculator from Google suggestions.
- And you will get the Simpson's Rule Calculator.

Now, add the values in the required fields to get the results.

## Benefits of Simpson's Rule Integral Calculator

The The Simpson's approximation calculator table has the following benefits:

- The simpsons rule calculator is fast and easier to use.
- It will approximate the integral in just a few minutes and solve the functions step by step.
- Simpson's Rule Calculator with steps keeps you away from complex and hectic manual calculations.
- This Simpson's method calculator can evaluate every possible definite functions with limits.
- It gives you the results in graphical form and comparision with exact area.
- The results of Simpson's rule integral calculator are reliable.
- It gives you accurate and authentic results.

So no doubt Simpson's Method Calculator has a a great tool for helping calculus students as well as teachers. Math is a home of complexicity but modern tools like laplace transform calculator and fourier transform calculator that make calculations easy and time saving for all.