Question

Approximate the following integrals using Gaussian quadrature with n= 2 and 3, Don't use computer, show the process! | a) | aº da b) (cos x dx Jo

Answer 1

Sotution 2 G=b-a 2 S O, 2 3 2S 2 SOts = b+G ° 947 L.O= Now (o.21/325 Jea) 0-2 1325)(0-21e tO 3615Į 3 {l7) = }[0-70967) (o-700676)eCo-708676) O.22700o O 5 XO.o 361S13 0 s X 2.027000 O6107S 684 01413500 OIS92 S6S Solution:- r) ('-) 2. Jaimi yn)= ne-

(14% Nou 61127ol LxCo41+o) X1 2 1.7749 - 0.e7298 C0.112701)e-(o.27a) 0.0112977 y)oe-os) - deoat © 1516327 gi)= (o-s07280)e-(oea7240) = 0.3241 3) S 2977 + y 0IS16327. 0-3 211629 ( (4- I1-(o.3211629) : 0.160591

TTy herr O392699 o 39269 9 C b+a O I6S97Y O 392699 Vs O 392699 0.39 2699 O 39 2699 b+a 2. O 619423 )=Cos) 2. cos (0165974oj Now 0.99999 2 01999 3 2 (o619423) Cos = O 39 26 S3 -39 26957 = O7534 Similaly peviows you Can do