What is the integral from 0 to 1/2 ln(3) of e^{2x} ?

The integral from 0 to 1/2 ln(3) of e^{2x} is 1

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integral from 0 to 1/2 ln(3) of e^{2x}

\int_{0}^{\frac{1}{2} l n (3)} e^{2 x} d x

1

Solution steps

\int_{0}^{\frac{1}{2} l n (3)} e^{2 x} d x

Apply u-substitution

= \int_{0}^{l n (3)} e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{l n (3)} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{0}^{l n (3)}

Compute the boundaries:

2

= \frac{1}{2} \cdot 2

Simplify

= 1

What is the integral from 0 to 1/2 ln(3) of e^{2x} ?
The integral from 0 to 1/2 ln(3) of e^{2x} is 1