Sketch the graphs of the functions. f(x) = x and g(x) = x2

Question

Find the area of the region completely enclosed by the graphs of the given functions f and g.

Answer 1

If you graph it, you see something like this:

The area we need to find is the light red (it's between f and g). An integral is the area under the graph so doesn't it make sense that the area we seek is ∫f - ∫g ?

Since we are dealing with the area between x = 0 and x = 1, we would use that as our limits of integration. You can do this manually or by using a calculator.

Do you understand how to proceed?