(a) Two function f(x) and g(x) are called orthogonal in the interval [ab] if they satisfy the condition Lf(x) g(x)dx = 0. Show that if f(x)=Lg(x)=x, then they are orthogonal in the interval [-1,1]. Determine the constants A and B so that the function h(x)=1+Ax+Bx², is orthogonal to fíx) and g(x) in the same interval.
(a) Two function f(x) and g(x) are called orthogonal in the interval [ab] if they satisfy the condition Lf(x) g(x)dx = 0. Show that if f(x)=Lg(x)=x, then they are orthogonal in the interval [-1,1]. Determine the constants A and B so that the function h(x)=1+Ax+Bx², is orthogonal to fíx) and g(x) in the same interval.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(a) Two function f(x) and g(x) are called orthogonal in the interval [ab] if they satisfy the condition
if(x) g(x)dx = 0. Show that if f(x)=L.g(x)=x, then they are orthogonal in the interval [-1,1]. Determine the
constants A and B so that the function h(x)=1+Ax+Bx², is orthogonal to f(x) and g(x) in the same interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a0b35ae-eb95-4093-af56-a89ee22ded45%2Fab0beb28-d74f-4b34-8e89-3f50abbb79c8%2Fikl0npk_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Two function f(x) and g(x) are called orthogonal in the interval [ab] if they satisfy the condition
if(x) g(x)dx = 0. Show that if f(x)=L.g(x)=x, then they are orthogonal in the interval [-1,1]. Determine the
constants A and B so that the function h(x)=1+Ax+Bx², is orthogonal to f(x) and g(x) in the same interval.
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