Given that $k$ is a positive constant, sketch the curve $E$ with equation $y=\left| {{x}^{2}}\left(

Question

Given that $k$ is a positive constant, sketch the curve $E$ with equation $y=\left| {{x}^{2}}\left( x-k \right) \right|$, labelling the coordinates of the points where the curve cuts the axes. [2] Hence, find, in terms of $k$, the area of the region(s) bounded by $E$ and the $x$-axis for $0\le x\le 2k$. [3]

Accepted Answer

$\frac{3}{2}k^4$

2024 NJC Promo Q3

2024 NJC Promo Q3

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