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Aim: How can we approximate the area under a curve using the Trapezoidal Rule?

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##### Aim: How can we approximate the area under a curve using the Trapezoidal Rule?

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**Aim: How can we approximate the area under a curve using**the Trapezoidal Rule? Do Now: Evaluate No can do! some elementary functions do not have antiderivatives that are elementary Fundamental Theorem of Calculus cannot be applied solution: must approximate**a**b x1 x2 x3 x4 The Trapezoidal Rule x0 x5 partition into equal subintervals**f(x0)**x1 f(x1) x0 The Trapezoidal Rule Area of 1st Trapezoid Area of ith Trapezoid Total Area is sum of all Trapezoids**a**b x1 x2 x3 x4 Total Area is sum of all Trapezoids The Trapezoidal Rule 1 2 3 4 5 x0 x5**a**b x1 x2 x3 x4 The Trapezoidal Rule 1 2 3 4 5 x0 x5**Trapezoidal Rule**Let f be continuous on [a, b]. The Trapezoidal Rule for approximating is given by**Model Problem**Use the Trapezoidal Rule to approximate and compare results for n = 4 and n = 8 0 0**Model Problem**n = 4 n = 8**left endpoint**right endpoint midpoint Approximation Rules**Trapezoidal Rule**Approximation Rules**Model Problem**16.328125