Let f and g be the functions given by #f(x)=e^x# and #g(x)=1/x#. What is the area of the region enclosed by the graphs of f and g between x=1 and x=2?
If we take a peek at the graphs of these functions, we'll see this:
Of course, we won't see that monstrous yellow blob - that's me. But what we need to concentrate on are the red graph (
To find it, all we need to do is find the area under
Mathematically, we express the area of the region like this:
Lucky for us, these two integrals are quite simple. Because the derivative of
Now it's on to evaluation:
An approximation to three decimal places is