Question

$\int\limits^1_0dx/eˣ+e⁻ˣ ,Evaluate the given integral expression:$

Answer 1

HELLO DEAR,


YOUR QUESTIONS IS----------------$\sf{\int\limits^1_0 dx/e^x + e^{-x}}$ ,Evaluate the given integral expression:


so, $\int\limits^1_0 \sf{{dx \over (e^x + {1\over e^x})}}$

$=\int\limits^1_0$ e^x . dx/(1 + e^{2x})

e^x = t => e^x.dx = dt
also, [x = 1 , t = e] and [x = 0 , t = 1]

$=\int\limits^e_1$ dt/(1 + t²)

$\sf{=[tan^{-1}x]^e_0}$

$\sf{=tan^{-1}e - \pi/4}$


I HOPE ITS HELP YOU DEAR,
THANKS