Question

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

Answer 1

`int_0^ln2e^xdx = 1`

Explanation:

`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`