# How do we solve this? I applied the fundamental theorem of calculus and know that f(x) = 1/x and n=b/a, but this is not the correct answer. Can someone please help? Thanks in advance

##### 1 Answer

Apr 30, 2018

#### Explanation:

You're correct that

#int_a^b 1/x dx = [ln x + C]_(x=a)^b#

#color(white)(int_a^b 1/x dx) = [ln b + C] - [ln a + C]#

#color(white)(int_a^b 1/x dx) = ln b + cancelC - ln a - cancelC#

#color(white)(int_a^b 1/x dx) = ln b - ln a#

We now wish this expression to equal

If we choose

#int_1^n 1/x dx = ln n - ln 1#

#color(white)(int_1^n 1/x dx) = ln n - 0#

#color(white)(int_1^n 1/x dx) = ln n#

This is valid for all