I'm not asking for answers.
I only ask about the bases, because I'm looking for some confirmation.
I will be doing the final answers, I want to do the final answers. I don't want anyone to have the glory of finding the final answer but me.
I just want to make sure that my methods are correct, that I'm heading in the right direction.
If you'd like I'll just go on what I'm thinking and post if it didn't work.
Part A: -8
Just got it using the trapezoid formula.
This now means that:
The other trapezoid is equal to the other one only it's positive 8$\displaystyle \(\int_{-5}^0 f(x) dx =-8\)$
Now I just need to figure out$\displaystyle \(\int_{5}^0 f(x) dx =8\)$
$\displaystyle \(\int_{5}^7 f(x) dx =\)$
It means that the integral is the negative of the area, not the area. Areas are never negative.
No, it is not. lengths are also never negative. The top base is 5 and the lower base is 3 not 4.And Base one is -5 and base two I believe is -4 correct?
The problem says "estimate" and there can be many equally good estimates to such a value. I might suggest using, not the area of a semi-circle, but the area of a semi-ellipse. If an ellipse has semi-axis lengths of a and b, then its area is $\displaystyle \pi ab$ and the area of half an ellipse is $\displaystyle \frac{1}{2}\pi ab$. The base across the parabola has length 2 so the semi-axis is 1. The depth of the parabola is 1 so that semi-axis is 1.And for the second one I think I have to add up all the areas, but what do I do for the parabola? Use Area of a semicircle formula?
However, on a closer look I see that the problem says "If the vertical red shaded area in the graph has area A" which makes me think you are supposed to give an answer in terms of "A", not actually find A. But then they wouldn't say "estimate" would they? I agree with undefined that B is not well defined.
Caution- the parabola is also below the x-axis.
Since -8+ 8= 0, I think it would be worth using one of your attempts to answer "-A"!