Calc Quiz Error Bound Formulas
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10 Terms
1
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Midpoint Error Bound
|E?| <= (k(b-a)³)/(24*n²)
|E?| = f’’(x)
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Trapezoidal Error Bound
|E?| <= (k(b-a)³)/(12*n²)
|E?| = f’’(x)
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Simpsons Error Bound
|E?| <= (k(b-a)^5)/(180*n^4)
|E?| = f^4(x)
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Left Endpoint
deltax[f(start)+…+f(n-1)]
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Right Endpoint
deltax[f(start+1)+…+f(n)]
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Midpoint
deltax[f(midpoints)+…+f(midpoints)]
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Trapezoid Rule
(deltax/2)*[f(start) + 2f(start + 1) + …+ 2f(n-1) + f(n)]
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Simpsons Rule
(deltax/3)*[f(start) + 4f(start+1) + 2f(start+2) + … +2f(n-2) + 4f(n-1) + f(n)]
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Length of curve
sqrt(1 + (y’)²)
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Area of curve
y = 2pi intergal(r * arclen) dx
r = y
arclen = sqrt(1 + (y’)²)
Note 
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