Help with curves please!

Question

Find the number b such that the line y = b divides the region bounded by the curves y = x² and y = 4 into two regions with equal area. Give your answer correct to 3 decimal places.

Answer 1

√ This will be easier if you integrate along the y-axis. For y=x^2 you use x = ∫√y which is the right half of the parabola. The two halves are symmetric so we can work on the right half only.

∫ √ydy from 0 to b = ∫ √ydy from b to 4yields    2/3y^3/2 from 0 to b  = 2/3 y^2/3 from b to 4

Solving this yields b = 4^2/3 = 2.52