面白い数学の問題おしえて～な 43問目

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S=π(R^2+r^2)
=π｛x^2(x^4+1)-2x^4√(x^4+1)+x^6+x^2(x^4+1)-6x^4√(x^4+1)+9x^6｝
f(x)=12x^6+2x^2-8x^4√(x^4+1)
f'(x)=72x^5+4x-32x^3√(x^4+1)-8x^4(1/2)(x^4+1)^(-1/2)・4x^3
=0
x=0.52737
S=π(R^2+r^2)
=π｛12・0.52737^6+2・0.52737^2-8・0.52737^4√(0.52737^4+1)｝
=0.5406704122……