Thread: Sketching the Graph of an Interval (Help Please)

Given first sketch the graph y = f(x) on the given interval.

Then find the integral of

f using your knowledge of area formulas for

rectangles, triangles and circles.

Originally Posted by evansf

Given first sketch the graph y = f(x) on the given interval.

Then find the integral of

f using your knowledge of area formulas for
rectangles, triangles and circles.

.. now, this can be separated to

..

we know, in the first addend, x is negative, hence we take |x| = -x; on the other hand, in the second addend, x is positive hence |x| = x

so the integral would be

now, we have to check where |1-x| is positive or negative and |1+x| is positive or negative..

for |1-x|, we take 1-x if 1-x >= 0 or x <= 1; we take x-1 otherwise

for |1+x|, we take 1+x if 1+x >= 0 or x >= -1; we take -x-1 otherwise

so now,



so can you do it now??

...

they are just linear functions, then they can easily be integrated.. Ü

Originally Posted by evansf

...

You might try posting a message in the message box, rather than just in the title.

Take a look at your graph. The integral is the total area between the function and the x axis. (Areas under the x axis count as negative.) As your function is composed of sections of straight lines, your areas are triangles. Easy to find the area of these.

-Dan