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