# Area bounded by curves

1. Feb 9, 2014

### BOAS

Hello,

quick question really.

1. The problem statement, all variables and given/known data

Find the area bound by the x axis, $x = 1$, $x = 4$ and $y = 2/x$

2. Relevant equations

3. The attempt at a solution

Representing this graphically, the question is equivalent to performing the definite integral of $y = 2/x$ from $1$ to $4$. Right?

Which would result in the area being equal to $2 ln(4)$

It seems painfully obvious but this question has made me doubt myself so I wanted to check I haven't missed anything obvious... i.e is there any reason to do the longhand of subtracting the smaller areas from the larger ones.

Thanks,

BOAS

2. Feb 9, 2014

### kduna

You are absolutely correct. I see no reason to put anything more than the integral you described. For any positive, integrable function, the area between the curve and the x-axis is equal to the definite integral of the function over the region concerned.