Mathematics

Mathematics

Problem

If Im,n=∫cos⁡mx sin⁡(nx) dxI_{m,n}=\int \cos^m x\,\sin(nx)\,dx, then 7I4,3−4I3,27I_{4,3}-4I_{3,2} is equal to (a) constant (b) −cos⁡2x+C-\cos^2 x+C (c) −cos⁡4xcos⁡3x+C-\cos^4 x\cos 3x+C (d) cos⁡7x−cos⁡4x+C\cos^7 x-\cos 4x+C (a) constant (b) −cos⁡2x+C-\cos^2 x+C (c) −cos⁡4xcos⁡3x+C-\cos^4 x\cos 3x+C (d) cos⁡7x−cos⁡4x+C\cos^7 x-\cos 4x+C

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