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877

Part of 2013 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 877

Source: 2005 Tokyo Gakugei University entrance exam/Education

6/17/2013
Let f(x)=lim⁡n→∞sin⁡n+2x+cos⁡n+2xsin⁡nx+cos⁡nxf(x)=\lim_{n\to\infty} \frac{\sin^{n+2}x+\cos^{n+2}x}{\sin^n x+\cos^n x} for 0≤x≤π2.0\leq x\leq \frac{\pi}2.
Evaluate ∫0π2f(x) dx.\int_0^{\frac{\pi}2} f(x)\ dx.
calculusintegrationlimittrigonometrycalculus computationsDefinite integrallimits