Find a continuous function

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Find a continuous function ff, (x4−4x2)≤f(x)≤(2x2−x3)(x^4 - 4x^2) \le f(x) \le (2x^2 - x^3) such that the area bounded by y=f(x)y = f(x), y=x4−4x2y = x^4 - 4x^2, the YY-axis and the line x=tx = t, (0≤t≤2)(0 \le t \le 2) is kk times the area bounded by y=f(x)y = f(x), y=2x2−x3y = 2x^2 - x^3, the YY-axis and the line x=tx = t, (0≤t≤2)(0 \le t \le 2).

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