- #1

- 217

- 0

**Evaluate definite integral. "x if x<1; 1/x if x> or equal to 1."**

1. Consider the function: f(x) = {x if x<1

{1/x if x≥1

Evaluate the definite integral.

∫from 0 to 4 of f(x)dx

2. Okay, I think I vaguely remember something about these sorts of problems... Isn't it something like you choose which value to go along with depending on what the limits of the integral are?

But the limit 0 goes along with "x if x<1" and 1 through 4 go along with "1/x if x≥1."

And integrals just evaluate area, so can we break this up into 2 integral problems?

__Integral #1__

∫0 to 0

Wait...But that would be just zero. If the limits were from 0 to 0, then there'd be no area! :/

__Integral #2__

∫1 to 4 of (1/x)dx

= ln(4) - ln(1) = 1.386

Yeah, this is not the right answer.

I don't even really know what I'm doing... =_=

I'm probably not even going about it right at all...

Help?

Thank you SO much!