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Question

The smaller area enclosed by y=f(x), where f(x) is polynomial of least degree satisfying [limx01+f(x)x3]1x=e and the circle x2+y2=2 above the xaxis is

A
π2+35
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B
π235
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C
π265
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D
None of these
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Solution

The correct option is A π2+35
Since limx0[1+f(x)x3]1x exists, so limx0f(x)x3=0
f(x)=a4x4+a5x5+...+anxn,an0,n4
Since, f(x) is of least degree f(x)=a4x4
The graph of y=x4 and x2+y2=2 are shown in the figure
The required area =210(2x2x4)dx=π2+35

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