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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x2+2x

x2+x+1

x2+2x+1

x3+1

answer is A.

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Detailed Solution

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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