Question

Find the number b such that the line y = b divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places.

Answer 1

Hello,

We may exchange x and y.
$-A_1= \int\limits^b_0 {x^2-1} \, dx = \dfrac{b^3}{3} -b\\ -A_2= \int\limits^1_b {x^2-1} \, dx =- \dfrac{2}{3} - \dfrac{b^3}{3}+b\\ -A_1=-A_2==\textgreater\ b^3-3b+1=0\\ sol={1.532088886238 , -1.879385241572 , 0.347296355334 }\\ The\ solution\ is\ 0.347296355334 .$≈0.347

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