Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of #y=4-x^2# and #y=1+2sinx#, how do you find the area?
In area problems, the first thing to do is graph the functions in question so you have a visual sense of the problem. You can check out the functions in this example graphed here.
From the graph, we see that the region
Putting this in math terms, we have:
The properties of integrals say we can split these two into mini-integrals like so:
Now we perform the integration:
And then evaluate: