Question

(15 pts Question 6: Evaluate the following integral: 1*(1 – e-x) dx (a) Analytically (b) Single application of the trapezoidal rule (e) Multiple-application trapezoidal rule, with n = 2 and 4

Answer 1

Solution) As per given in the question by using various methods to find the integration we can see that analytically we get the exact answer but with the trapezoidal rule we get an approximate answer which approaches to the exact answer as value of n is increased or we can say that the no. of steps is increased as observed in the solution below-

- Integral of 0-2) - a) Analytically & Iz sien (x-04-1)" (x + e 4te-y_o-eo - 4+0.01831-1 2 3.01831 x=4 b) Single application of trapezoid rule No yol0%.98169 i-ex_1-0 Hoo ne 4, 1-841-0.0183120 198169 I. ( yotyn) (0+0.98169)1.96338 (C) Multiple application trapezoidal rele n = 2 24. when ng h=2 : 20 x=2 x=4 420 421-e2 y = 0.98169. e2 2 - 1202247 0.981691 0.86466 -- I h ( Yo +241+ 42) 2210+ 210.8466) to .98169) 2.71102 9-1-es 29 7-9 ryzo 20.639 12 g , X-3 8466 Zzz 1-e3 20.95021 x=4, 44= 0.98/69 +0.98169) I. ( 4o 148,+9z+13)+44) $(0+2(0-63211 +0-86466 +0 99021) 45.87567 2.9378