find the definite integral of int[4, 9] [ 6/x ] dx

[jself]

I can not figure out how to find the integral since the problem is dealing with division.

(integral sign) 9 at the top, 4 at the bottom (6/x) dx

I am not asking for the answer. I just need to know how to get started on this problem. I know you are so supposed to show work, but I am not sure how to get started.

 

[tkhunny]

For x > 0, the antiderivative of 1/x is ln(x). That's all you need. You didn't cover that in class?

 

[jself]

Yes, actually I did read that in the textbook. I take online courses so I didn't have someone explaining what that meant. I thought it was only ln(x) if it was 1/x, not any number over x.

 

[stapel]

I thought it was only ln(x) if it was 1/x, not any number over x.

Just take the constant out front:

. . . . .\(\displaystyle \L \int\, \frac{a}{x}\, dx\, =\, a\, \int\, \frac{1}{x}\, dx\)

Integrate in the usual way, and then multiply the constant "a" back in.

Eliz.