Question

QUESTION 5 The integral 2 1 I= dx x +4 0 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite Trapezoidal rule, given by -haf" (), a< & <b, 12 is less than 10-5 for the approximation of I. b - a (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are ci = 1, i = 1, 2; r1 = 0.5773502692, r2 = -0.5773502692) (c) Evaluate the integral analytically and find the error in the approximation in (a) above.

Answer 1

( 1 ) solution: (5a, f(x) = 1 Cathy 2 (+43 mat lpkool - og god So, 23 L10-5 12N² N> 45.64 N=46 hy oooh b x=t+1 s f(x) dx = { ft+D dt [f(140) + f (10.) -0.1792966107 +0.2261087947 -0.405405 405 0405405

1 Station de = (lo (nty))" In (8)-In(u) = ln (2) -0-6931471806 -0.69314718 60800 0.27742
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