Question

The value of $\frac{8}{\pi} \int\limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x$ is

Answer 1

The correct answer is 2.
I=π8​0∫2π​​(sinx)2023+(cosx)2023(cosx)2023​dx......(1)
Using 0∫a​f(x)dx=0∫a​f(a−x)dx
I=π8​0∫2π​​(sinx)2023+(cosx)2023(sinx)2023​dx........(2)
Adding (1) & (2)
2I=π8​0∫2π​​1dx
I=2