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Trapezoidal & Riemann Sums
AP Calculus AB · Unit 6 Integration
Learning Objectives
Approximate definite integrals using rectangles and trapezoids
Compare Left, Right, Midpoint, and Trapezoidal rules
Observe error decreasing as n increases
Understand over/underestimates based on concavity
Trapezoidal Rule
T = (Δx/2)[f(x₀) + 2f(x₁) + ... + 2f(xₙ₋₁) + f(xₙ)]
Δx = (b−a)/n
Average of Left and Right sums
Tags
trapezoidal
Riemann
numerical integration
FUNCTION
f(x) = x² [0,2]
f(x) = sin(x) [0,π]
f(x) = eˣ [0,1]
f(x) = 1/x [1,5]
METHOD
Left
Right
Midpoint
Trapezoid
Subintervals n
4
Approximation
—
Exact
—
Error
—
% Error
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