Let r be the region enclosed by the graph of y=x^2 and the line y=4
If the line x=a divides region r into two regions of equal area ,find a.

If the line y=b divides the region r into two regions of equal area ,find b.

Question

Let r be the region enclosed by the graph of y=x^2 and the line y=4
 If the line  x=a divides region r into two regions of equal area ,find a.

If the line y=b divides the region r into two regions of equal area ,find b.

anonymous · Answer

i know this function is a parabola., with line at y=4
so the area is everthhing from -2 to 2

amistre64 · Answer

the first part is trivial at best; since you know its a parabola (and parabolas are symmetric about their vertex).

the second part is more challenging; we would need to know the total are of the region to begin with so that we can integrate it up to half

anonymous · Answer

ok i got the total area already
i
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anonymous · Answer

it is 32/3

amistre64 · Answer

$$2\int_{0}^{b}\sqrt{x}\ dx=\frac{total. area}{2}$$

amistre64 · Answer

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