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Today's calculation of integral 89

Source: 1986 Fukushima Medical University entrance exam

November 16, 2005
calculusintegrationtrigonometryfunctionsymmetrycalculus computations

Problem Statement

For f(x)=x4+∣x∣,f(x)=x^4+|x|, let I1=∫0πf(cos⁡x) dx, I2=∫0π2f(sin⁡x) dx.I_1=\int_0^\pi f(\cos x)\ dx,\ I_2=\int_0^\frac{\pi}{2} f(\sin x)\ dx. Find the value of I1I2.\frac{I_1}{I_2}.
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