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857

Part of 2012 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 857

Source: 1970 Tokyo Medical and Dental University entrance exam

12/17/2012
Let f(x)=lim⁡n→∞(cos⁡nx+sin⁡nx)1nf(x)=\lim_{n\to\infty} (\cos ^ n x+\sin ^ n x)^{\frac{1}{n}} for 0≤x≤π2.0\leq x\leq \frac{\pi}{2}.
(1) Find f(x).f(x).
(2) Find the volume of the solid generated by a rotation of the figure bounded by the curve y=f(x)y=f(x) and the line y=1y=1 around the yy-axis.
calculusintegrationlimittrigonometrygeometrygeometric transformationrotation