Question 5 Numerical Integration Starting Definition Lagrange Inter Polation Polynomials D Q43790603
QUESTION 5 (a) Numerical Integration: Starting from the definition of the Lagrange inter- polation polynomials derive the Trapezoidal rule – namely: I(S) =[F(x0) + f(11)] where I (f) is the integral. (10 marks] (b) Numerical Integration: Compute the value of the integral of the two func- tions f(x) = 2 + 9x and f(0) = 3 over the interval x € (0,3) in both cases. Explain any differences between the exact value and the value computed by using the Trapezoidal rule defined in Q5(a) above. [10 marks] Show transcribed image text QUESTION 5 (a) Numerical Integration: Starting from the definition of the Lagrange inter- polation polynomials derive the Trapezoidal rule – namely: I(S) =[F(x0) + f(11)] where I (f) is the integral. (10 marks] (b) Numerical Integration: Compute the value of the integral of the two func- tions f(x) = 2 + 9x and f(0) = 3 over the interval x € (0,3) in both cases. Explain any differences between the exact value and the value computed by using the Trapezoidal rule defined in Q5(a) above. [10 marks]
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Answer to QUESTION 5 (a) Numerical Integration: Starting from the definition of the Lagrange inter- polation polynomials derive th…
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