Find the bounds of two functions containing an absolute value

Question

We were given the two functions $f_1(x) = |x|$ and $f_2(x) = x^2-2$ of which we needed to find the surface of. My solution this far is:

However, I don't know which bounds I have to use for my integral. When I plotted the graph on my graphic calculator the two bounds were $-2$ and $2$, but I don't know how I could possibly find them without.

Any help is appreciated.

People who make the effort to help you with your question would appreciate it if you also make the effort to post the pictures with the correct orientation. — wimi, Jan 05 '20 at 10:36

score 1 · Accepted Answer · answered Jan 05 '20 at 11:09

1

You have already found the bounds. You have written:

First case, $x\ge 0$: $$x^2-x-2=0\implies\begin{cases}x=2\\x=-1\end{cases}$$ But this first case requires $x\ge 0$ (see two lines above), so the only valid solution is $x=2$.
Second case, $x\le 0$: $$x^2+x-2=0\implies\begin{cases}x=1\\x=-2\end{cases}$$ But this second case requires $x\le 0$ (see two lines above), so the only valid solution is $x=-2$.

There go your two bounds.

answered Jan 05 '20 at 11:09

wimi

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Oh I didn't even pay attention to the condition, my bad. Thank you lots! – LLScheme Jan 05 '20 at 11:47

Find the bounds of two functions containing an absolute value

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