Integral Calculator
Free Integral Calculator for calculus. Enter values to get step-by-step solutions with formulas and graphs. See charts, tables, and visual results.
Reviewed by Manoj Kumar, Mathematics Educator
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Simpson's Rule: โซf(x)dx โ (h/3)[f(xโ) + 4f(xโ) + 2f(xโ) + 4f(xโ) + ... + f(xโ)]
Simpson's 1/3 rule uses quadratic interpolation for numerical integration. It requires an even number of subintervals. Error is O(hโด), making it much more accurate than the trapezoidal rule for smooth functions.
Worked Examples
Example 1: โซxยฒ from 0 to 1
Problem:f(x) = xยฒ, bounds [0, 1]
Solution:โซxยฒdx = xยณ/3 |โยน = 1/3 = 0.33333333
Result:0.33333333
Example 2: โซsin(x) from 0 to ฯ
Problem:f(x) = Math.sin(x), bounds [0, 3.14159265]
Solution:โซsin(x)dx = [-cos(x)] from 0 to ฯ = (-cos(ฯ)) - (-cos(0)) = 1 - (-1) = 2
Result:โ 2.00000000
References
Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy