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

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

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integral from 0 to t of 3e^x

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

3 (e^{t} - 1)

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

e^{t} - 1

= 3 (e^{t} - 1)

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