Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y = 9 into two regions with equal area. (Round your answer to two decimal places.)

Answer 1

We want

Int(x dy)[0,b] = Int(x dy)[b,9]

x = 1/4 y^(1/2)

Int(y^(1/2))[0,b] = Int(y^1/2)[b,9]

2/3 y^(3/2)[0,b] = 2/3 y^(3/2)[b,9]

2/3 b^(3/2) = 2/3 9^(3/2) - 2/3 b^(3/2)
4/3 b^(3/2) = 2/3 9^(3/2)
2b^(3/2) = 9^(3/2)
2^(2/3) b = 9
b = 9/2^(2/3) = 9/cbrt(4)