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`

Explanation

To find the continuous function \( f(x) \) that satisfies the given conditions, we will follow these steps:

### Step 1: Set up the area equations
We need to find the area bounded by \( y = f(x) \), \( y = x^4 - 4x^2 \), the y-axis, and the line \( x = t \) for \( 0 < t < 2 \). The area can be expressed as:
\[ A_1 = \int_0^t (f(x) - (x^4 - 4x^2)) \, dx \]

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