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Today's calculation of Integral 66４

Source:

January 12, 2011
calculusintegrationtrigonometrycalculus computations

Problem Statement

For a positive integer nn, let In=∫−ππ(π2−∣x∣)cos⁡nx dxI_n=\int_{-\pi}^{\pi} \left(\frac{\pi}{2}-|x|\right)\cos nx\ dx.
Find I1+I2+I3+I4I_1+I_2+I_3+I_4.
1992 University of Fukui entrance exam/Medicine
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