Solutions to Math 421 QUIZ #4


Decide whether the following pair of functions f(x), g(x), with  the weight w(x)  over the given interval are orthogonal.
EXPLAIN

(1) (5 pts) f(x)=x, g(x)=x^2, w(x)=1, interval=(-1,1)

Sol. int(f(x)*g(x)*w(x),x=-1..1)= int(x^3,x=-1..1)= x^4/4 |_{-1,1}= 1^4-(-1)^4=0

Since this integral is 0 the answer is YES.


(2) (5 pts) f(x)=x, g(x)=1, w(x)=x, interval=(2,3)

Sol. int(f(x)*g(x)*w(x),x=-1..1)= int(x^2,x=2..3)= x^3/3 |_{2,3}=(3^3-2^3)/3=19/8

Since this integral is NOT 0 the answer is NO.