What is the integral from 3 to 6 of 7e^y ?

The integral from 3 to 6 of 7e^y is 7(e^6-e^3)

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integral from 3 to 6 of 7e^y

\int_{3}^{6} 7 e^{y} d y

7 (e^{6} - e^{3})

Decimal

2683.40279 \dots

Solution steps

\int_{3}^{6} 7 e^{y} d y

Take the constant out:

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

= 7 \cdot \int_{3}^{6} e^{y} d y

Use the common integral:

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

= 7 [e^{y}]_{3}^{6}

Compute the boundaries:

e^{6} - e^{3}

= 7 (e^{6} - e^{3})

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What is the integral from 3 to 6 of 7e^y ?
The integral from 3 to 6 of 7e^y is 7(e^6-e^3)