Question

If the line $y=b$ divides the region bounded by the curves $y=x^2$ and $y=9$ into regions of equal area, then the value of $b$ is

• A. $\frac{3}{\sqrt[3]{34}}$
• B. $\frac{5}{\sqrt[3]{34}}$
• C. $\frac{7}{\sqrt[3]{34}}$
• D. $\frac{9}{\sqrt[3]{34}}$

Answer 1

The correct option is D $\frac{9}{\sqrt[3]{34}}$


$2{\int }_0^b\sqrt{y}dy=2{\int }_b^9\sqrt{y}dy\Rightarrow {\left(\frac{2y^{\frac{3}{2}}}{3}\right)}_0^b={\left(\frac{2y^{\frac{3}{2}}}{3}\right)}_b^9\Rightarrow b^3=\frac{3^6}{4}\Rightarrow b=\frac{9}{\sqrt[3]{34}}$