Calculate definite integral

Compute ∫ₐᵇ f(x) dx for polynomials using Simpson's rule.

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Inputs

Coefficients (constant, x, x², …)

Lower limit a

Upper limit b

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∫_0.0000^2.0000 f(x)dx

18.285714

Exact (polynomial): 18.285714

∫(x^6) dx from 0.0000 to 2.0000

Steps

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Compute ∫ₐᵇ f(x) dx for polynomials using Simpson's rule. ∫ₐᵇ f(x)dx = F(b) − F(a) where F′ = f.

∫ₐᵇ f(x)dx = F(b) − F(a) where F′ = f.

∫₀² x² dx = 8/3 ≈ 2.667.

Numeric vs exact?+

Polynomials show exact FTC result; Simpson confirms numerically.