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A polynomial $P$ is positive for $x > 0,$ and the area of the region bounded by $P (x),$ the x-axis, and the vertical lines $x = 0$ and $x = K$ is $K^{2} (K + 3) / 3$ .The polynomial $P (x)$ is

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Correct option is A

We have ∫0K P(t)dt=K2(K+3)3 Differentiatingw.r.t K, we get P(K)=K23+2K3(K+3)=K2+2K.

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A polynomial P is positive for x > 0, and the area of the region bounded by P (x), the x-axis, and the vertical lines x = 0 and x=K isK2(K+3)/3.The polynomial P(x) is

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free study material

A polynomial $P$ is positive for $x > 0,$ and the area of the region bounded by $P (x),$ the x-axis, and the vertical lines $x = 0$ and $x = K$ is $K^{2} (K + 3) / 3$ .The polynomial $P (x)$ is