Question

Written Essay on Module 4: Applications of Integration & Numerical Integration, Due May 2 5. (10 points) For both graphs below, use (i) Trapezoidal Rule, and (ii) Simpson's Rule with a sub- division into n = 4 subintervals to estimate the area under the given curves on the interval (1,5). (iii) In each case, determine which rule is more accurate. Explain why. (a) y = f(x) (b) y = g(x)

Answer 1

The al ses so sx = Salt subinterval's are (1,2), (2,3), (3,4], [us] Tu = ax (FC) & a f(2) & 2 F(3) + f(u) + f(s)) = { [o + a + 4 + 6 + 4) = 8 o Su - on [FCI) + 4 F(2) + f(3) + 4 fcu) + f(s)) - Ś Co + 4 + 4 + 1a + 4) = P = 8 © Tu - DX (4 + 2 + 0 +9+u] = 12 -6 su – I s u + 4 to + 4 + 4 = 16 - 5.3333 Simpson's Rule is more accurate.