A Simpson’s rule calculator approximates the value of a definite integral by fitting parabolas through points on the curve. Enter the function, the interval and an even number of subintervals, and it calculates the approximation and shows each step. It’s often much more accurate than the trapezoidal rule with the same number of points.
The formula is ∫ₐᵇ f(x) dx ≈ (Δx ÷ 3) × [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + … + 4f(xₙ₋₁) + f(xₙ)], where Δx = (b − a) ÷ n and n must be even. The coefficients follow the pattern 1, 4, 2, 4, 2, …, 4, 1.
Example: approximate ∫₀² x² dx with n = 4. Δx = 0.5, and the points are 0, 0.5, 1, 1.5 and 2, with values 0, 0.25, 1, 2.25 and 4. Simpson’s rule gives (0.5 ÷ 3) × [0 + 4(0.25) + 2(1) + 4(2.25) + 4] = (1/6) × 16 = 2.667. The exact answer is 8/3 ≈ 2.667, a perfect match, because Simpson’s rule is exact for polynomials up to degree three.
Tips: always use an even number of subintervals, organize your work in a table and increase n for better accuracy with complicated functions. Simpson’s rule is used in engineering and science to integrate data points when there’s no formula for the function.
How to use the Simpson’s Rule Calculator on Minedit: enter your values in the fields, press calculate, and review the step-by-step breakdown under the result. If something looks off, change one input at a time to see how it affects the answer, which is also a great way to learn the math behind it.
Why use an online Simpson’s Rule Calculator: it saves time, avoids simple arithmetic mistakes and shows each step, so you can check your homework, plan a project or make a decision with confidence. Bookmark the page so it’s ready the next time you need it.
Learn more on Wikipedia’s Simpson’s rule article. Find integral, Euler’s method and double integral calculators on Minedit.