10) Use Gauss-Legendre 1-point formula and 2-point formula to evaluate 1 1+x² dr.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please do 3 questions. It needs very urgently so do it 10,11 do it in gauss legendre 1,2,3 point formula. And 12 please do. First mention whats the formula of gauss legendre 1,2,3 point form. I give u like.
1
(10) Use Gauss-Legendre 1-point formula and 2-point formula to evaluate f
1
(11) Using Gauss-Legendre 3-point formula, evaluate (i)
(0) / -dx (ii)
1+x
1
+x2
dx.
x²+2x+1
1.5
+ (x + 1)2 dx (iii) fe-z² dx.
0.2
h
(12) Determine the values of a, b and e such that the formula fƒ(z)dx = h [aƒ(0) + bƒ (3) + cf(h)]
is
exact for polynomials of as high degree as possible.
Transcribed Image Text:1 (10) Use Gauss-Legendre 1-point formula and 2-point formula to evaluate f 1 (11) Using Gauss-Legendre 3-point formula, evaluate (i) (0) / -dx (ii) 1+x 1 +x2 dx. x²+2x+1 1.5 + (x + 1)2 dx (iii) fe-z² dx. 0.2 h (12) Determine the values of a, b and e such that the formula fƒ(z)dx = h [aƒ(0) + bƒ (3) + cf(h)] is exact for polynomials of as high degree as possible.
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