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I am looking for the area bounded between the following curves:

$y=x^{2},y=\frac{x^{2}}{2},y=2x$

I have used the computer to draw these easy to draw functions:

enter image description here

And it appears that no area is bounded by the three curves. What should I do then, calculate the area between the red and green functions only?

Thank you.


After you told me to zoom out, I did:

enter image description here

This is the new graph. Should I calculate only the right area, not the one between red and green?

So from 0 to 2, I do an integral of green above blue and from 2 to 4 red above blue?

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    $\begingroup$ You should zoom out. $\endgroup$ – DHMO Apr 17 '17 at 10:54
  • $\begingroup$ the searched area is between the red, green blue curve $\endgroup$ – Dr. Sonnhard Graubner Apr 17 '17 at 11:03
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$y=2x$ cuts $y=x^2$ at $x=2$ and $y=x^2/2$ at $x=4$ So from the zoomed out figure, you must understand why the required answer is to integrate $x^2-x^2/2$ from $0$ to $2$ and $2x-x^2/2$ from $2$ to $4$ and add the two results.

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