Question

Let f and g be the functions given by f(x)=e^x and g(x) = ln x.
Find the area of the region enclosed by the graphs of f and g between x = 1/2 and x=1.

Answer 1

\[\int\limits\limits_{.5}^{1} (upper function-lower function) dx\]

Answer 2

on that interval
\[\ln(x)\] is negative and
\[e^x\] is positive, so if you want the area between them you can integrate
\[-\int_{\frac{1}{2}}^1\ln(x)dx+\int_{\frac{1}{2}}^1e^xdx\]

Answer 3

yep upper function is the e^x
and the lower function is ln(x)

Answer 4

or what myininaya says. it amounts to the same thing

Answer 5

the only hard one is the first one.
\[\int_.5^1e^xdx=e-\sqrt{e}\]

Answer 6

'anti derivative" of log is
\[x\ln(x)-x\] so that one is not so hard either

Answer 7

there are 2 parts to this question...can u help me with te hsecond part too?

Answer 8

so is the final asnwer xln(x) - x + (e - sqrt of x)