A curve y = f(x) is such that f(x)ge 0 and f(0)=0 and bounds a curvilinear triangle with the base [0,x] whose area is proportional to (n+1)^(th) power of f(x)cdot" If "f(1)=1 then find f(x).

A curve y = f(x) is such that f(x)ge 0 and f(0)=0 and bounds a curvili

1.	A curve y = f(x) is such that f(x)ge 0 and f(0)=0 and bounds a curvilinear triangle with the base [0,x] whose area is proportional to (n+1)^(th) power of f(x)cdot" If "f(1)=1 then find f(x).
Answer» Solution :ACCORDING to the question `OVERSET(x)underset(0)intf(x)dx=lamda{F(x)}^(n+1)` Where `lamda` is constant of proportionality Differentiating both sides w.r.t x, `f(x)=lamda(n+1)(f(x))^(n)f'(x)` `"or "(f(x)^(n-1))f'(x)=(1)/(lamda(n+1))` Integrating both sides w.r.t x, `((f(x))^(n))/(n)=(x)/(lamda(n+1))+C` `f(0)=0, THEREFORE C=0` `(f(x))^(n)=(nx)/(lamda(n+1))` `f(1)=1` `therefore""(n)/(lamda(n+1))=1` `therefore""f(x)=x^(1//n)`

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A curve y = f(x) is such that f(x)ge 0 and f(0)=0 and bounds a curvilinear triangle with the base [0,x] whose area is proportional to (n+1)^(th) power of f(x)cdot" If "f(1)=1 then find f(x).

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