🧮 Fraction Integral Calculator
Compute definite integrals of rational functions using numerical methods. Select a function, adjust bounds, and see the area under the curve. Compare Trapezoidal, Simpson, and Midpoint rules.
Step 1: Function & Interval
50
0.5
About the integral
Choose a rational function. For functions like 1/(x²+p²) the parameter p scales the denominator. Avoid singularities (e.g., x=0 for 1/x, x=±1 for 1/(x²−1)).
Step 2: Integration Settings
5
Numerical integration
Approximates ∫f(x)dx from a to b. Simpson’s rule requires even n. Results may be less accurate near singularities.
Definite Integral Result
Summary
Method Comparison
Area & Analysis
Approximate Integral ∫ f(x) dx
1.83
Method: Trapezoidal (n=50)
Function
1/x
Interval [a,b]
[1.0, 5.0]
Parameter p
0.5
Est. error
±0.002
Comparison of Integration Methods
| Method | Approx. Integral | Error estimate | n (intervals) |
|---|
Function plot with area under curve
Integral interpretation
The shaded area represents the definite integral. Use the parameter slider to explore families of rational functions.
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