From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

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 50/CH5/EX5.16/ex_5_16.sce | 16 ++++++++++++++++
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 create mode 100755 50/CH5/EX5.16/ex_5_16.sce

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diff --git a/50/CH5/EX5.16/ex_5_16.sce b/50/CH5/EX5.16/ex_5_16.sce
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+// example 5.16
+// caption: gauss-legendre three point method
+// I= integral 1/(1+x) in the range [0,1];
+// first we need ti transform the interval [0,1 ] to [-1,1], since gauss-legendre three point method is applicable in the range[-1,1],
+
+// let t=ax+b;
+// solving for a,b from the two ranges, we get a=2; b=-1; t=2x-1;
+
+// hence I=integral 1/(1+x) in the range [0,1]= integral 1/(t+3) in the range [-1,1];
+
+
+deff('[y]=f(t)','y=1/(t+3)');
+// since , from gauss legendre three point rule(n=2);
+I=(1/9)*(5*f(-sqrt(3/5))+8*f(0)+5*f(sqrt(3/5))) 
+
+// we know , exact solution is ln 2=0.693147;
\ No newline at end of file
-- 
cgit