Question

solve the following questions with steps​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Let

$i = \int_{0} ^{ \frac{\pi}{2} } \frac{ {e}^{ \sin(x) } }{ {e}^{ \sin(x) } + {e}^{ \cos(x) } } dx \\ substiute \: \: x \: \: \to \: \: \frac{\pi}{2} + x \\ (property \: \: a + b - x) \\ i = \int_{0} ^{ \frac{\pi}{2} } \frac{ {e}^{ \cos(x) } }{ {e}^{ \sin(x) } + {e}^{ \cos(x) } } dx \\ add \: \: both \\ \\ 2i = = \int_{0} ^{ \frac{\pi}{2} } \frac{ {e}^{ \sin(x) }{+ {e}^{ \cos(x) } } }{ {e}^{ \sin(x) } + {e}^{ \cos(x) } } dx \\ 2i = \int_{0} ^{ \frac{\pi}{2} } 1.dx = \frac{\pi}{2} \\ i = \frac{\pi}{4}$