Thread: definite integral

need help plz

Originally Posted by gracy

need help plz

In shorthand:


so


-Dan

Hello, gracy!

Make some sketches and use baby-talk . . .

and
Find:

The first integral says: the area under from 0 to 1 is square units.
The graph might look like this.

Code:

        |
        *
        |   *
        |     *
        |  7   *
        |
      --+-------*----
        |       1 
        |

The second integral says: the area under from 0 to 3 is only

How did we lose some area?
Some of the area from 1 to 3 must be negative.
. . The graph must dip below the x-axis.

The graph might look like this.

Code:

        |
        *
        |   *
        |     *
        |  7   *
        |               3
      --+-------*-------+--
        |       1 *  -3 :
        |           *   :
        |               *

And that is why: .