Riemann Sum Visualizer
∫03 x² dx
Function & Limits
Riemann Method
Left
Right
Midpoint
Trapezoidal
Results
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Riemann Sum
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Exact Integral
Error |Riemann − Exact|
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Relative error
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Method
Left
Width Δx
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FTC Breakdown
F(b) − F(a) = ∫f(x)dx
Area Interpretation
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Preset Integrals
Fundamental Theorem of Calculus:
∫ab f(x) dx = F(b) − F(a)
where F′(x) = f(x)
Riemann Sum (Left):
S = Δx · Σ f(xi), xi = a + iΔx
Trapezoidal Rule:
T = Δx/2 · [f(a) + 2Σf(xi) + f(b)]
∫ab f(x) dx = F(b) − F(a)
where F′(x) = f(x)
Riemann Sum (Left):
S = Δx · Σ f(xi), xi = a + iΔx
Trapezoidal Rule:
T = Δx/2 · [f(a) + 2Σf(xi) + f(b)]