What is the integral from 0 to ln(2) of e^{x+y} ?

The integral from 0 to ln(2) of e^{x+y} is e^x

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integral from 0 to ln(2) of e^{x+y}

\int_{0}^{l n (2)} e^{x + y} d y

e^{x}

Solution steps

\int_{0}^{l n (2)} e^{x + y} d y

e^{x + y} = e^{x} e^{y}

= \int_{0}^{l n (2)} e^{x} e^{y} d y

Take the constant out:

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

= e^{x} \cdot \int_{0}^{l n (2)} e^{y} d y

Use the common integral:

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

= e^{x} [e^{y}]_{0}^{l n (2)}

Compute the boundaries:

1

= e^{x} \cdot 1

Simplify

= e^{x}

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What is the integral from 0 to ln(2) of e^{x+y} ?
The integral from 0 to ln(2) of e^{x+y} is e^x