Integral Question?

Question

http://img131.imageshack.us/my.php?image=tyya7.png

Please look at that question (above). Would g(1) be referring to the green or black triangle? In terms of area they are the same, but conceptually which one is it referring 2?

Also for g(x) to [2,3] Why is only the shaded box included but not the white box underneath?

Answer 1

g(1) would be referring to the green triangle. Remember that the integral is the signed area _between_ the curve and the x axis. In this case, that happens to be above the curve, thus the area is negative (if the region between the curve and the x-axis is below the curve, then the area is positive. It may be easier to remember this if you think of the integral as being negative over any region where the function itself is).

The reason why the white box is not included is that it is not between the curve and the x-axis. I'm a bit perplexed as to the source of your confusion.

Answer 2

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