Numerical Integration Calculator
Approximate the area under a curve using the trapezoidal rule.
Enter a function f(x), bounds, and number of intervals.
Approximate Area
Trapezoidal Rule approximates a definite integral by dividing the area into trapezoids.
Formula:
∫ f(x) dx ≈ (h/2) × [f(x₀) + 2f(x₁) + 2f(x₂) + ... + 2f(xₙ₋₁) + f(xₙ)]
Where:
- h = (b - a) / n (width of each interval)
- a = lower bound, b = upper bound
- n = number of intervals (more = more accurate)
Supported functions:
- Basic:
x^2,2*x + 3,x^3 - x - Trig:
sin(x),cos(x),tan(x) - Other:
sqrt(x),log(x)(natural log),exp(x),abs(x) - Constants:
pi,e
Accuracy: Error decreases as n increases. Doubling n roughly quadruples accuracy for smooth functions. For most purposes, n = 100 to 1000 gives good results.