the x-intercepts for both functions are
c and -c
If you look at your sketch there is symmetry about the y-axis as well, so we could just take our area from 0 to c
4∫(c^2 - x^2) dx = 230 from 0 to c
∫(c^2 - x^2) dx
= [c^2 x- (1/3)x^3] from 0 to c
= (c^3 - (1/3)c^3 - 0
= (2/3)c^3
4(2/3)c^3 = 230
c^3 = 86.25
c = 4.418...
check my arithmetic
Find c>0 such that the area of the region enclosed by the parabolas y=x2−c2 and y=c2−x2 is 230.
1 answer