Find the number b such that the line $y=b$ divides the region bounded by the curves $y=x^{2}$ and $y=5$ into two regions with equal area.
A) $5^{1 / 2}$
B) $5^{2 / 3}$
C) $\frac{2}{3}$
D) $5^{1 / 3}$
E) $\frac{1}{3}$

Question

Quizplus · Accepted Answer

The total area between $y=x^2$ and $y=5$ from $x=-\sqrt{5}$ to $x=\sqrt{5}$ is 10/3. To divide this area equally, each region should have an area of 5/3. Solving the integral of $5-b$ from $-\sqrt{b}$ to $\sqrt{b}$ equal to 5/3 gives $b=5^{2/3}$.

Find the Number B Such That the Line y=by=by=b Divides the Region Bounded by the Curves

Find the Number B Such That the Line $y=b$ Divides the Region Bounded by the Curves