Find the continuous function `f` where `(x^4-4x^2)lt=f(x)lt=(2x^2-x^3)` such that the area bounded by `y=f(x),y=x^4-4x^2dot` then y-axis, and the line `x=t ,` where `(0lt=tlt=2)` is `k` times the area bounded by `y=f(x),y=2x^2-x^3`,y-axis , and line `x=t(w h e r e0lt=tlt=2)dot`

Answer

`f(x)=1/(k+1)[x^4-kx^3+(2k-4)x^2]`