Solve integrals using flexible interval and method controls. Create tables and export clean results instantly. Check weights, steps, subintervals, and area estimates with confidence.
This sample uses f(x) = x² from 0 to 4 with h = 1.
| Index | x | f(x) |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 4 |
| 3 | 3 | 9 |
| 4 | 4 | 16 |
For an even number of subintervals, use:
Integral ≈ (h/3) × [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + f(xn)]
For subintervals in multiples of three, use:
Integral ≈ (3h/8) × [f(x0) + 3f(x1) + 3f(x2) + 2f(x3) + ... + f(xn)]
Auto mode uses Simpson 1/3 first. It then applies Simpson 3/8 on the last three subintervals when needed.
Simpson rule is a trusted numerical integration method. It estimates the area under a curve. It works well when an exact antiderivative is hard to find. It also performs better than simple rectangle or trapezoid estimates in many smooth cases.
This calculator supports function input and table input. That makes it useful for classwork, engineering tasks, and data analysis. You can test a formula directly. You can also enter measured points from an experiment. Both routes return a clean approximation table and a final integral estimate.
The tool includes Simpson 1/3, Simpson 3/8, and an automatic mixed option. Simpson 1/3 needs an even number of subintervals. Simpson 3/8 needs subinterval counts that are multiples of three. Auto mode handles odd counts by combining both methods. This saves time and reduces manual trial work.
Simpson formulas assume equally spaced points. The calculator checks that condition for table input. It also builds the sample points automatically for function input. That keeps the method valid and the output consistent. Clear validation messages help you correct mistakes fast.
The result section appears below the header and above the form. You can review the chosen method, step size, points, and final approximation quickly. The generated table shows each x value, the related y value, and a helpful detail note. CSV export supports spreadsheet review. PDF export supports reporting and sharing.
Use this calculator for calculus homework, numerical methods practice, and sampled lab data. It is useful when you need a quick, structured approximation. It is also helpful when you want to compare interval choices and method rules. Short steps, direct outputs, and clean layout make the process easier.
It estimates a definite integral. In simple terms, it approximates the area under a curve using weighted sample points.
Use Simpson 1/3 when your point spacing is equal and the number of subintervals is even. It is often the default choice.
Use Simpson 3/8 when your subinterval count is a multiple of three. It is also useful in mixed Simpson calculations.
It applies Simpson 1/3 where possible and then uses Simpson 3/8 on the final three subintervals when the total count is odd.
Yes. Choose table input, then enter equally spaced x values and matching y values. The calculator will validate the spacing first.
Composite Simpson formulas rely on a constant step size. Unequal spacing breaks the rule and leads to invalid approximations.
You can use expressions such as sin(x), x^2 + 3*x, sqrt(x), log(x), exp(x), and abs(x). Use explicit multiplication.
They export the current result summary and generated data table. This is useful for records, reports, and spreadsheet checks.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.