Answer :

y = x4 – 2x3 + x2 + 3


y’ = 4x3 – 6x2 + 2x


At extrema of y, y’ = 0


i.e., 4x3 – 6x2 + 2x = 0


or, 2x3 – 3x2 + x = 0


x(2x – 1)(x – 1) = 0


i.e., x = 0, x = 1/2 and x = 1 correspond to extrema of y


Now, y’’ = 12x2 – 12x + 2


y’’0 = 2 > 0 x = 0 corresponds to a minima


y’’1/2 = -1 < 0 x = 1/2 corresponds to a maxima


y’’1 = 2 > 0 x = 1 corresponds to a minima


So, x = 0 and x = 1 are the ordinates we need.


So, the area A is –


A =


=




(Ans)

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