What is the integral from 0 to 3 of 4e^x ?

The integral from 0 to 3 of 4e^x is 4(e^3-1)

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integral from 0 to 3 of 4e^x

\int_{0}^{3} 4 e^{x} d x

4 (e^{3} - 1)

Decimal

76.34214 \dots

Solution steps

\int_{0}^{3} 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_{0}^{3} e^{x} d x

Use the common integral:

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

= 4 [e^{x}]_{0}^{3}

Compute the boundaries:

e^{3} - 1

= 4 (e^{3} - 1)

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What is the integral from 0 to 3 of 4e^x ?
The integral from 0 to 3 of 4e^x is 4(e^3-1)