I don't think I really understand what I am doing. This topic has me a little befuddled, so please bear with me.
First, how do you correctly express the integration of a constant? (And no, my text does not explain this. I have looked several times.)
As in:
I understand that the answer is 10 (the area bound by the lines and ) but not how to obtain or express that answer using the definite integral.
Does not seem to make sense when f(x) is a constant.
Thanks for the help! Integration may be my waterloo.
In a definite integral (i.e., with limits for the variable(s) that you're integrating with respect of), there are no integration constants.
Example:
and now you evaluate the function, in virtue of Barrow's Rule:
In the other hand, if your integral is where for some in the domain of the function.
EDIT: Ok, bad english.I'm sorry, I didn't looked as well as I should to your question
Let me give you an example.
Let's say we have , this gives us .
Expanding this we get .
You could also double check this by drawing the graph of and finding the area between 0 and 5, this would give you a rectangle with sides of 3 and 5, giving you the area 15.
Does this explain it a bit more?
It possible that we use different notation, I had never come across the symbol before.
In mine above, the first one is the integral of 3 with respect to x, between x equals 5 and 0.
The second with the square brackets is when I have integrated the equation, and the limits upper and lower limits are placed at the top and bottom of the last square brackets respectively.
This is how I have been taught them anyway, if you have been taught different the continue to use the way that feels best for you.
Flipping ahead a few lessons in my book I found "The First Fundamental Theorem of Calculus" (very portentious, huh?) which basicly states that the definite integral can be computed the way you show. I think that since that is further along than I am, it is only expected that I compute it as an area -- but your way is much easier. Thanks again for all of the help!