Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 16 into two regions with equal area. (Round your answer to the nearest hundredth.)

Answer 1

the line y = b intersects y = x^2 at (√b,b), and the line y = 16 cuts it at (4,16)

so we want
integral[b - x^2)dx from 0 to √b = (1/2)integral[16 - x^2] from 0 to 4

(bx - x^3/3) from 0 to √b = (1/2)[16x - x^3/3] from 0 to 4

b√b - b√b/3 = (1/2)(64 - 64/3)

b√b - b√b/3 = 64/3
2b√b = 64
b√b = 32
b^3 = 1024
b = 10.0794

b = 10.08 correct to 2 decimals