The smaller area enclosed by y=f(x), where f(x) is polynomial of least degree satisfying [limx→01+f(x)x3]1x=e and the circle x2+y2=2 above the x−axis is
A
π2+35
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B
π2−35
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C
π2−65
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D
None of these
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Solution
The correct option is Aπ2+35 Since limx→0[1+f(x)x3]1x exists, so limx→0f(x)x3=0
∴f(x)=a4x4+a5x5+...+anxn,an≠0,n≥4
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 =2∫10(√2−x2−x4)dx=π2+35