What is the integral from 0 to ln(2) of e^x-e^{-x} ?

The integral from 0 to ln(2) of e^x-e^{-x} is 1/2

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integral from 0 to ln(2) of e^x-e^{-x}

\int_{0}^{l n (2)} e^{x} - e^{- x} d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{l n (2)} e^{x} - e^{- x} d x

Rewrite using trig identities

= \int_{0}^{l n (2)} 2 sinh (x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{l n (2)} sinh (x) d x

Use the common integral:

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

= 2 [cosh (x)]_{0}^{l n (2)}

Compute the boundaries:

\frac{1}{4}

= 2 \cdot \frac{1}{4}

Simplify

= \frac{1}{2}

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What is the integral from 0 to ln(2) of e^x-e^{-x} ?
The integral from 0 to ln(2) of e^x-e^{-x} is 1/2