Calculus
Simpson's Rule Calculator
Approximate definite integrals numerically. Use Simpson's 1/3 Rule or the Trapezoidal Rule to approximate the area under a curve using numerical integration techniques.
d/dx
Examples:
Differentiation Rules
Power Rule
d/dx [x^n] = nx^(n-1)
Product Rule
[fg]' = f'g + fg'
Chain Rule
d/dx [f(g(x))] = f'(g(x))g'(x)
Constant Rule
d/dx [c] = 0
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Solution Methodology
01
Calculate Step Size (h)
Divide the interval length (b-a) by the number of subintervals (n).
02
Generate Data Table
Calculate the function value f(x) at each subinterval point.
03
Apply Weighting Formula
Multiply the y-values by the Simpson's 1-4-2-4-1 pattern and sum the results.
Common Questions
What is Simpson's Rule?
Simpson's Rule is a numerical method for approximating a definite integral. Instead of connecting points on the curve with straight lines (like the Trapezoidal rule), it connects groups of three points with parabolas, yielding a much more accurate approximation for smooth curves.
Why does Simpson's Rule require an even number of intervals?
The standard Simpson's 1/3 Rule works by fitting a parabola to three consecutive points (which span two subintervals). Therefore, the total number of subintervals (n) across the entire integration range must be an even number.