Definate Integrals from a graph.

[fraiha]

2 is above and 0 is below (sorry I don't know the Tex to do that symbol).
So it'd look at like [ g(x)dx. And y = g(x)

There's a graph with a straight line, a semicircle, and another straight line all connected. There's 3 parts to the question, A, B, C. I assumed, to find the straight lines I take g(x) = mx+b and that I have to get the slope and y-intercept from the graph. And I'm assuming I'd use pi*r for the semicircle. My problem is I cannot get the correct answer for a one or two parts, while the other part it comes out correct. I'm pretty sure this is because I don't know what the two X's (2,0) actually mean in regards to the graph. Such as, if x = 5 and 10 is the Y-Intercept where x = 5 is? If there's multiple slopes between x=5 and x=10 do I just find the slope by using (y2-y1)/(x2-x1). Otherwise I understand that [ G(2)=(mx+b) - G(0)=(mx+b). Thanks for any help![/tex]

 

[pka]

It is doubtful that any of us can follow your description of the problem.
If you need help, see if you can scan the actual problem and post it.
At the top of this page is ‘Forum Help’: the first item is ‘Inserting Images’.

 

[fraiha]

So let b = 2 and a = 0.

So then g(x) = mx+b and if there was a semicircle g(x) = pi*r. To get the slope I would use (x2 - x1)/(y2 - y1) which would -> (2 - 0) / (2 - 0). To get the y-intercept I would look at x = 0 and see where the line starts which would be b = 0. So then I just find the antiderivative and plug it into the first function. But what if there were multiple slopes in that graph and 'b' and 'a' covered the entire graph from start to finish. Sort of like this

The page (lamar.edu) says to use

What if the graph has 3 or more different slopes (or shapes)? Also, how would I find the function of a curve? For most of this I just assumed this is what I have to do as I have no real examples so I was wondering if anyone can confirm any of what I just said. Thanks for the help![/img][/list]