Kalkulator Integral

Hitung integral tentu dan visualisasikan luas di bawah kurva dengan arsiran region. Pahami integrasi secara visual.

∫ Area Under Curve
∫
Enter a function and bounds, then compute the integral

Coba contoh ini

Classic
∫₀³ x² dx
Result: 9
Trig
∫₀ᵖⁱ sin(x) dx
Result: 2
Gaussian
∫₋₂² e^(-x²) dx
≈ √π approximation
Odd function
∫₋₁¹ (x³ - x) dx
Result: 0 (symmetric)
📚 What is an Integral?

Understanding Integration

The definite integral ∫ₐᵇ f(x) dx represents the net signed area between the function curve and the x-axis, from x = a to x = b.

∫ₐᵇ f(x) dx = F(b) − F(a), where F'(x) = f(x)

Key concepts:

  • Area above x-axis (where f(x) > 0) contributes positively
  • Area below x-axis (where f(x) < 0) contributes negatively
  • Fundamental Theorem of Calculus: integration and differentiation are inverse operations
  • Indefinite integral: the antiderivative F(x) + C (where C is any constant)

This calculator uses Simpson's Rule for numerical integration — a highly accurate method that fits parabolic arcs to the curve.

❓ FAQ

Frequently Asked Questions

A negative result means the curve is primarily below the x-axis between your bounds. The integral measures signed area — area below the x-axis counts as negative.
C is the constant of integration. Since the derivative of any constant is 0, infinitely many antiderivatives exist (each differing by a constant). Use initial conditions to find the specific C.
This uses composite Simpson's Rule with 1000 intervals, which is extremely accurate for smooth functions. Error is typically on the order of 10⁻¹⁰ or smaller.