What is the integral from 0 to ln(3) of e^{x+y} ?

The integral from 0 to ln(3) of e^{x+y} is e^x*2

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integral from 0 to ln(3) of e^{x+y}

\int_{0}^{l n (3)} e^{x + y} d y

e^{x} \cdot 2

Solution steps

\int_{0}^{l n (3)} e^{x + y} d y

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

= \int_{0}^{l n (3)} 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 (3)} e^{y} d y

Use the common integral:

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

= e^{x} [e^{y}]_{0}^{l n (3)}

Compute the boundaries:

2

= e^{x} \cdot 2

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\int_{0}^{1} 6 x^{2} y d x

\int_{0}^{0.5} e^{x^{2}} d x

What is the integral from 0 to ln(3) of e^{x+y} ?
The integral from 0 to ln(3) of e^{x+y} is e^x*2