What is the integral from 0 to a of cosh(t/a) ?

The integral from 0 to a of cosh(t/a) is ((e^2-1)a)/(2e)

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integral from 0 to a of cosh(t/a)

\int_{0}^{a} cosh (\frac{t}{a}) d t

\frac{( e ^{2} - 1 ) a}{2 e}

Solution steps

\int_{0}^{a} cosh (\frac{t}{a}) d t

Apply u-substitution

: \int_{0}^{1} cosh (u) a d u

= \int_{0}^{1} cosh (u) a d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= a \cdot \int_{0}^{1} cosh (u) d u

Use the common integral:

\int cosh (u) d u = sinh (u)

= a [sinh (u)]_{0}^{1}

Compute the boundaries:

\frac{e ^{2} - 1}{2 e}

= a \frac{e ^{2} - 1}{2 e}

Simplify

= \frac{( e ^{2} - 1 ) a}{2 e}

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What is the integral from 0 to a of cosh(t/a) ?
The integral from 0 to a of cosh(t/a) is ((e^2-1)a)/(2e)