Question

Find the area bounded by the parabola y=(1/2)x^2 and the hyperbola y^2-x^2=8. state your answer exactly.

Answer 1

If you solve for \(y\) in the hyperbola, you get: \[
y=\pm \sqrt{x^2+8}
\]

Answer 2

Both equations are symmetric across the \(y\) axis, you can can integrate one section and double the result.

Answer 3

so then \[(1/2)x^2 \pm \sqrt{x^2 +8} = 0\]

Answer 4

You'll want to integrate with respect to \(y\) too, since this is a \(y\) simple area.

Answer 5

Nope.

Answer 6

I don't need intercepts?

Answer 7

You need to find points of intersection to find limits of integration.

Answer 8

Hold on, graph it first.

Answer 9

Okay so it looks like this: