(f(x) − g(x)) dxIn order to determine whether one of the curves is above the other, we can graph them on the
calculator.
The graph looks like the following:
As we can see, the graph of y = 2 ln x is above y = on the entire interval, so all we have to
do is evaluate the integral dx =.Step 2: We can do the integration one of two ways—on the calculator or analytically.
Calculator: Evaluate fnint = 3.498
Analytically: dx = 2 ln x dx − x dx =
2 (x ln x − x) − ≈ 18.498 − 15 = 3.498You can use the formula ln x dx = x ln x − x, or you can do it as one of the basic integration-
by-parts integrals.(b) Set up, but do not integrate, an integral expression, in terms of a single variable, for the