Advanced Integral Calculator
Enter a function, integration variable, and limits. Adjust subintervals for Simpson’s rule to evaluate the integral.
| Example | Function f(x) | Variable | Lower Limit (a) | Upper Limit (b) | Subintervals | Expected Result (approx.) | Action |
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Virtual Formula Pad
Below is a comprehensive list of formulas. Scroll to see more. Click “Copy” to copy the formula into the function input.
| Formula | Action |
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What is an Integral Calculator?
An integral calculator computes the definite integral of a function over a given interval. Integration is the process of finding the area under a curve and is essential in fields such as physics, engineering, economics, and statistics.
Practical Applications
- Calculating displacement from velocity in physics.
- Determining total revenue over a period in economics.
- Computing work done by a variable force in engineering.
- Evaluating probabilities using density functions in statistics.
- Analyzing energy consumption in electrical engineering.
Frequently Asked Questions (FAQ)
What is the difference between definite and indefinite integrals?
A definite integral calculates the area under a curve between two limits, yielding a numerical result. An indefinite integral represents the family of antiderivatives, including a constant of integration.
How accurate is numerical integration using Simpson’s rule?
Simpson’s rule is highly accurate for smooth functions when a sufficient number of subintervals is used. For functions with discontinuities or rapid oscillations, its accuracy may vary.
Can this calculator handle improper integrals?
This calculator is designed for proper integrals with finite limits. Improper integrals require special handling that is not implemented here.
Why do I need to enter an even number for subintervals?
Simpson’s rule approximates the integrand using parabolic segments over pairs of subintervals, which requires an even number of subintervals for proper calculation.
Which libraries does this calculator use?
It uses Math.js for parsing and evaluating mathematical expressions and Plotly.js for creating interactive graphs.