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7 Cards in this Set

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Left-hand rectangle approximation
Ln = ΔX(f(Xo) + f(X1) +...+ f(Xn-1) = ΔXsum(f(Xk), n-1, k=0)
Right-hand rectangle approximation
Rn = ΔX(f(X1) + f(X2) +...+ f(Xn) = ΔXsum(f(Xk), n, k=1)
Midpoint Rule
f(a+ΔX(k+1/2)) = f((Xk+Xk+1)/2)
Total Area: Mn=ΔX(f((X0+X1)/2)+...f((Xn-1+Xn)/2) = ΔXsum(f((Xk+Xk+1)/2),n-1,k=0)
Trapezoidal Rule
Area of Trapezoid= ΔX/2 (f(Xk)+f(Xk+1))
Tn=ΔX/2(f(Xo)+2f(X1)+2f(X2)+...+2f(Xn-1)+f(Xn))
Simpson's Rule
Sn=ΔX/3 (f(X0)+4f(X1)+2f(X2)+4f(X3)+...+2f(Xn-2)+4f(Xn-1)+f(Xn)
ΔX
(b-a)/n
Riemann Sums
ΔXsum(f(Xk),n-1,k=0), where Xk is any sample ppoint in the kth subinterval