Numerical Integration: Trapezoid ruleObjective: to approximate the integral on a given interval [a,b].Assumption: f(x) is a scalar-valued function of x and has a continuous second derivative.To find the linear polynomial which interpolates (a,f(a)) and (b,f(b)), we can use LiliLagrange interpolation:baxbfbbxaf))(())((aa
Trapezoid ruleWe integrate the Lagrange polynomial from a to b, with the result:).()()(21abbfafExample1: Use the trapezoid rule to approximate the integral of f(x)=x2on interval [1,2].5.212)2()1(2/1ffThe actual value is 7/3= 2.33
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