What is the integral from-4 to 4 of-e^{1/4 x} ?

The integral from-4 to 4 of-e^{1/4 x} is -4(e-1/e)

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integral from-4 to 4 of-e^{1/4 x}

\int_{- 4}^{4} - e^{\frac{1}{4} x} d x

- 4 (e - \frac{1}{e})

Decimal

- 9.40160 \dots

Solution steps

\int_{- 4}^{4} - e^{\frac{1}{4} x} d x

Take the constant out:

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

= - \int_{- 4}^{4} e^{\frac{1}{4} x} d x

Apply u-substitution

= - \int_{- 1}^{1} e^{u} \cdot 4 d u

Take the constant out:

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

= - 4 \cdot \int_{- 1}^{1} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - 4 [e^{u}]_{- 1}^{1}

Compute the boundaries:

e - \frac{1}{e}

= - 4 (e - \frac{1}{e})

What is the integral from-4 to 4 of-e^{1/4 x} ?
The integral from-4 to 4 of-e^{1/4 x} is -4(e-1/e)