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

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

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

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

0

Solution steps

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

Apply Integration By Parts

: [e^{2 x} x - \int 2 e^{2 x} x d x]_{l n (2)}^{l n (2)}

= [e^{2 x} x - \int 2 e^{2 x} x d x]_{l n (2)}^{l n (2)}

\int 2 e^{2 x} x d x = e^{2 x} x - \frac{1}{2} e^{2 x}

= [e^{2 x} x - (e^{2 x} x - \frac{1}{2} e^{2 x})]_{l n (2)}^{l n (2)}

Simplify

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

Compute the boundaries:

0

= 0

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