Question

How do you evaluate the integral `int_1^(4)1/xdx` ?

Answer 1

The answer is `ln4`.

Recall that the FTC is a powerful statement; it allows us to compute area under the curve just by finding antiderivatives. So the best thing that you can do for yourself is to make a reference sheet with the common antiderivatives, then practice using them and hopefully you can commit them to memory.

If you try to use the power rule for this integrand you will run into trouble because you will get `x^0/0`; this should be a clue that the power rule is not what you want. Instead, you need to use `int 1/x dx=ln|x|+C`. So,

`int_1^4 1/x dx`
`=lnx|_1^4`
`=ln4 - ln1`
`=ln4 - 0`
`=ln4`