Approximate the definite integral of a function using trapezoids.
Integration Parameters
f(x) = x²
Currently visualizing f(x) = x². The trapezoidal rule works for any function by connecting sample points with straight lines.
Approximation Result
22.0000
Integral Area
Calculated using linear interpolation between points.
Step Size (Δx)1.0000
Intervals4
About this calculator
What is the Trapezoidal Rule?
The Trapezoidal Rule is a numerical method for approximating the definite integral of a function. It works by dividing the area under a curve into several trapezoids rather than rectangles (used in Riemann sums). This usually provides a more accurate approximation of the area, especially for smooth curves.
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Pro Tips
Δx = (b - a) / n is the width of each trapezoid.
Increasing 'n' (the number of subintervals) generally leads to a more accurate result.
This rule assumes the function is linear between each sampled point.
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Fun Facts
"The Trapezoidal Rule belongs to a family of methods called Newton-Cotes formulas."
"It is equivalent to integrating the linear interpolant of the function."
"In many engineering applications, sensors sample data at intervals, making the trapezoidal rule a natural choice for integrating signals."
