Question

2. The following integral 2 dr can be computed exactly (a) Estimate the integral using the composite trapezoidal rule with n = exact value of integral and compute the true percent relative error for this approximation 4. Calculate the (b) How many subintervals would be needed to estimate the integral with the composite trapezoidal rule with an accuracy of 102? (c) Estimate the integral using the composite Simpson's 1/3 rule with n = true percent relative error for this approximation 4. Compute the (d) How many subintervals would be needed to estimate the integral with the composite Simpson's 1/3 rule with an accuracy of 10 2?

Answer 1

n4 (0.693)" x 45 . 1081180 n9 : n 131-20 131-20 n = 3-38 the composite 102 using Simpson's rude 3 sub we need intervals.

14:0, buy ini all Dhe bran: 40:1 '. Ý : a = 0 x = 8th otlat x = , + h: 14:2 #3: X2 th: 2+1=3 X4 X2th = 3+1=4 fly): 20 flyi); [a]'. ! flxv) a ll fles); a n8 fl8y): 91: 16 Trapi doi dal yule :- 7/4): flyg)# if(x) + df (8) fgfl®3) then ) tot 2(0)+ a14) +218) + 16)

) * 18 - Action ( 33.683 -14) : [a1443)

True relative Error 21643 -2) 1643 6.643 21643 - 0019

b) from theor u s the error for the componite fi (bag) e pe second de mi vati ve POF F(x) = I loves) An(21) 2* il ( 10:121) >* fi 1012 , it has maximum at 7:0 1289 löta (4)? x 10.693) 121912 .10.073) 10² x 12 14) **70-693).na 4) * x 10.693) 10²x12 30-735936 x 102 nr: n 12 mo183 x 10 n: 1:10 X10 (n: 11 n... we need : Il sub intervals.

simpson's ils nule. 8(4): fixed t 4.4(4) +af/ XL) +48/43) + 10+ 4(1) +2 143 +9 (6) +86] True zvryov i 21.643-20 21.643 0.015 d) The amor for the composite simpson's rule. is : (-9). . 18ony it the de fivative of flut: il menyap Ei jod jól. 14.0)" campo)" an 102. u 10.603) . 18ong the 180 n4