Problem

Source: Moldova National MO 2008, 12 Grade, Problem 2

Tags: integration, trigonometry, real analysis, real analysis unsolved



Find the exact value of $ E=\displaystyle\int_0^{\frac\pi2}\cos^{1003}x\text{d}x\cdot\int_0^{\frac\pi2}\cos^{1004}x\text{d}x\cdot$.