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Question

The area bounded by y=f(x)=x42x3+x2+3, X-axis and ordinates corresponding to minimum of the function f(x) is

A
130
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B
110
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C
9130
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D
3
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Solution

The correct option is A 9130
The given curve is y=x42x3+x2+3
dydx=4x36x2+2x
d2ydx2=12x212+2
For maxima and minima dydx=0
4x36x2+2=0
x=0,1,12
d2ydx2x=0=2,d2ydx2x=12=1 and d2ydx2x=1=2
Therefore point of minima are x=0 and x=1
Therefore required area =10(x42x3+x2+3)dx
=(x552x44+x33+3x)10=9130.

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