# Solving a polynomial equation over a range of $x$?

$$\left.\left(\frac{2x^3}{3} - 4x^2 + 10x\right) \right|_1^3 = 12 - 20/3$$

I guess my first question would be what is the meaning of the line in this equation. I was under the impression it is meant to represent a range of x values. However I'm not sure how both sides are equal or how one would go about solving this.

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@Peter Tamaroff. I thank you with all my heart. – Michael Gruber Sep 7 '12 at 0:27
$f(x) |_{x_0}^{x_1} = f(x_1) - f(x_0)$ – user2468 Sep 7 '12 at 0:31

This is typically used when solving definite integrals.

It means $f(3) - f(1)$, so:

$f(3) = (2/3)*27 - 4(9) + 10(3) = 12$, and

$f(1) = (2/3)*1 -4(1) + 10(1) = 20/3$

therefore $(12 - 20/3)$.

Note: be careful writing $2/3x^3$ because it could be incorrectly interpreted.

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$$f(x)\bigr|^b_a$$ is notation for $f(b)-f(a)$.

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