dbt...

let f(x) be a differentiable function satisfying (x-y)f(x+y)-(x+y)f(x-y)= 4xy(x²-y²) for all x,y belongs to R . f(1) = 1 then....

1. the area of the region bounded by the curves y=f(x) and y=x² is....

2. the value of âˆ«_-1^² f(x) dx is........

2 Answers

first of all u need to get the fn which is very simple in this case...by simple manipulation u getf(x) x-x²=k

=>f(x)=kx-x³
given f(1)=1

=>1=k-1 =>k=2

=>f(x)=2x-x³

now can u complete it ??

eure u hav done a mistake...after ur first step

2nd step bears d result f(x)=kx+x^3

at f(1)=1
k=0

therefore f(x)=x^3

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