What is the integral from-2 to 0 of-4e^x ?

The integral from-2 to 0 of-4e^x is -4(1-1/(e^2))

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integral from-2 to 0 of-4e^x

\int_{- 2}^{0} - 4 e^{x} d x

- 4 (1 - \frac{1}{e ^{2}})

Decimal

- 3.45865 \dots

Solution steps

\int_{- 2}^{0} - 4 e^{x} d x

Take the constant out:

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

= - 4 \cdot \int_{- 2}^{0} e^{x} d x

Use the common integral:

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

= - 4 [e^{x}]_{- 2}^{0}

Compute the boundaries:

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

= - 4 (1 - \frac{1}{e ^{2}})

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What is the integral from-2 to 0 of-4e^x ?
The integral from-2 to 0 of-4e^x is -4(1-1/(e^2))