Find the area bounded by the curve #y=2x^2-6x# and #y=-x^2+9#?
First, it is a good idea to graph the given curves:
We need to evaluate the area bounded by these curves, i.e find the area in between them.
That's the area between their points of intersection, so we need to find that: their points of intersection:
We don't really need to find the points of intersection; the
This is because the curves are already specified in terms of
Now we can start evaluating the definite integrals of these curves in the interval
Therefore, the area bounded by the curves is