Finding the Area Bounded by Curves | Quick Solution

[BOAS]

Hello,

quick question really.

Homework Statement

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

Homework Equations

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

 

[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.