I'm super confused about what is going on here. I got an email from my prof with an explanation that left me even more lost. Here's the question:
Let f(x) =
0 if x<-4
4 if -4<= x < -1
-5 if -1 <= x < 4
0 if x >= 4
g(x) = int_(x at top, -4 at bottom) f(t) dt
Determine the following:
g(0) = ?
g(5) = ?
The absolute maximum of g(x) occurs when x = -1 at what value?
The explanation from my prof used things like "m1(a-b) and m2(b-x)" but I have no idea what this means. Could someone please explain to me the process of solving this? I tried just figuring out that when x = 0 the answer (given above) is -5, but this isn't right.
I have very little idea what that means. What I was hoping for was an explanation of what was going on and how to find an answer. I do not know what to do with what you have given me, although I am grateful for the help. Perhaps an English explanation?
Recall that an integral represents the net area under a curve.
So when we look at , we are finding the net area under the curve from to . This should be fairly easy by considering as we are essentially working with straight line segments. No complicated formulas here besides that of finding the area of a rectangle.
Note that it was split into 2 integrals in order to work with both line segments individually.