Area bounded by ln(x) and x-2?

Question

How do you calculate the area bounded by ln(x) and x-2?
As I can't solve ln(x)=x-2 I'm not sure what to do here.

Note: I said "bounded by" and I wasn't supposed to use anything more than an ordinary calculater for this.

Answer 1

You're trying to equate them. What you really need to do is take their difference and then take the integral of that term:

A = ∫(lnx - (x-2))dx = ∫lnx dx - ∫(x-2)dx

Looks a little easier now, eh?

There's still a problem. To find the limits of integration, you have to solve the 2 eqns simultaneously to get the intersection points. I don't think there is an algebraic way to do that, so here are the limits (determined numerically); x = .158594 and x = 3.1465

Answer 2

You're thinking too hard. It's just the area under ln(x) minus the area under x-2.

Keep in mind that for integration areas can be negative.