Integration Calculator

Use JavaScript math syntax. For example: Math.sin(x), Math.exp(x), x*y, etc.
Result: ---

Integration Examples

  • Single Integration:

    Function: x*x (from 0 to 1)

    Result: 0.333333 (approximately ⅓)

  • Double Integration:

    Function: x*y (x: 0 to 1, y: 0 to 1)

    Result: 0.250000 (approximately ¼)

  • Trigonometric:

    Function: Math.sin(x) (from 0 to Math.PI)

    Result: 2.000000

Numerical Integration Methods

Trapezoidal Rule

This calculator uses the trapezoidal rule for numerical integration. It approximates the definite integral by calculating the area under a curve using trapezoids.

Multiple Integration

For double and triple integrals, we use multiple applications of the trapezoidal rule across each dimension.

Common Integration Formulas

  • ∫ xn dx = (xn+1)/(n+1) + C
  • ∫ sin(x) dx = -cos(x) + C
  • ∫ cos(x) dx = sin(x) + C
  • ∫ ex dx = ex + C
  • ∫ 1/x dx = ln|x| + C