What is the integral from 1 to 2 of 3e^x ?

The integral from 1 to 2 of 3e^x is 3(e^2-e)

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integral from 1 to 2 of 3e^x

\int_{1}^{2} 3 e^{x} d x

3 (e^{2} - e)

Decimal

14.01232 \dots

Solution steps

\int_{1}^{2} 3 e^{x} d x

Take the constant out:

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

= 3 \cdot \int_{1}^{2} e^{x} d x

Use the common integral:

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

= 3 [e^{x}]_{1}^{2}

Compute the boundaries:

e^{2} - e

= 3 (e^{2} - e)

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What is the integral from 1 to 2 of 3e^x ?
The integral from 1 to 2 of 3e^x is 3(e^2-e)