Expert: Paul Klarreich - 4/20/2006

Question
My name is Lisa and I am studying integration. We were given a problem that had a graph and it listed many different integrals and it said define these integrals using this graph. It gave the integral symbol, and a interval, and to the right of the symbol it had dx. I didn't know how to solve it?

Answer
Hi, Lisa,
I think I need more information, such as a picture, or the integrals, or something else.  BUT in general, you would define a definite integral as an area under a curve.  So if you are looking at the graph of

y = f(x)

and at the integral

{7
|    f(x) dx
}3

you might say this is the area bounded by:
  the graph of y=f(x) on top
  y = 0  on the bottom.
  x = 3 (a vertical line) on the left
  x = 7 on the right.

Does that help?