zzzzzz 10th grade u 12yr old
it is e
ecuation of first circle equation - second
you're looking at the negative because its all below x axis. look at negative of big circle which is integral from -1 to 1 of -(sqrt(9-x^2)) (call this g) and then subtracting the semi-circle which is -sqrt((1-x^2)) (call this f)
so: g-f to find area and you get sqrt(1-x^2) - (sqrt(9-x^2)
and you can workout formula of circle easily by x^2+y^2 = r^2 where r is radius. you can rearrange to find y by -x^2 and taking + and - sqrt. discard the + sqrt because you're only looking below the x-axis
You want to subtract the two circles to find the area between. Since you're taking the bottom part of the integral, you want to take the negative parts of the square roots. So you'd take the integral from -1 to 1 of -sqrt(9-x^2) - (-sqrt(1-x^2)), which if you simplify out comes out to C.
Not C as the result is negative.