Solve for: integral from 0 to 1 of 2cosh(x) x

Expression: $\int_{ 0 }^{ 1 } 2\cosh\left({x}\right) \mathrm{d} x$

To evaluate the definite integral first evaluate the indefinite integral

$\int{ 2\cosh\left({x}\right) } \mathrm{d} x$

Use the property of integral $\begin{array} { l }\int{ a \times f\left( x \right) } \mathrm{d} x=a \times \int{ f\left( x \right) } \mathrm{d} x,& a \in ℝ\end{array}$

$2 \times \int{ \cosh\left({x}\right) } \mathrm{d} x$

Use $\int{ \cosh\left({x}\right) } \mathrm{d} x=\sinh\left({x}\right)$ to evaluate the integral

$2\sinh\left({x}\right)$

To evaluate the definite integral, return the limits of integration

$\left. 2\sinh\left({x}\right) \right|_{ 0 }^{ 1 }$

Use $\left. F\left( x \right) \right|_{ a }^{ b }=F\left( b \right)-F\left( a \right)$ to evaluate the expression

$2\sinh\left({1}\right)-2\sinh\left({0}\right)$

Simplify the expression

\begin{align*}&e-\frac{ 1 }{ e } \\&\approx2.3504\end{align*}

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