How do you evaluate the definite integral $int e^x$ from $[0,ln2]$ ?

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Answer 1 · 2016-11-02T17:11:23

$int_0^ln2e^xdx = 1$

$e^x$ is the only function which remains unchanged when differentiated, and consequently $inte^xdx=e^x+C$

So, $int_0^ln2e^xdx = [e^x]_0^ln2$
$:. int_0^ln2e^xdx = e^ln2-e^0$
$:. int_0^ln2e^xdx = 2-1$
$:. int_0^ln2e^xdx = 1$

How do you evaluate the definite integral int e^xint e^x from [0,ln2][0,ln2]?