Find the number b such that the line
y = b
divides the region bounded by the graphs of
y = 16x2
and
y = 4
into two regions with equal area. (Round your answer to two decimal places.)
b =
since the graphs meet at (±1/2,4), and using the symmetry about the y-axis, we can use
∫[0,b] 1/4 √y dy = ∫[b,4] 1/4 √y dy
or, you can go the long way around and use
∫[0,1/4 √b] (b-16x^2) dx = (4-b)(1/4 √b) + ∫[1/4 √b,1/2] (4-16x^2) dx