# Area bounded by these lines and curves

1. May 5, 2006

### Reshma

Find the area of a figure bounded by the equilateral hyperbola $xy = a^2$, the x-axis, and the lines $x = a$, $b = 2a$.

My work:
The equations of the lines and curves involved here are:
$$xy = a^2$$
$$y = 0$$
$$x = a$$
I don't know how b=2a is treated as an equation of a line here & hence I am puzzled as how to get the limits for the definite integral here. Well the formula I tried using is(Q stands for area):
$$Q = \int_a^b [f_1(x) - f_2(x)]dx$$

Guidance needed.

2. May 5, 2006

### neutrino

I guess it's a typo. It's probably x = 2a.

3. May 6, 2006

### Reshma

Thanks, you are right!
$$y = {a^2\over x}$$
$$Q = \int_a^{2a} {a^2\over x} = a^2\ln 2$$

...which tallies with the solution given .