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Say I have a function

$$V(x)=A(x-x_1)(x-x_2)(x-x_3)$$

where $x_1$, $x_2$, $x_3$ are the three roots in increasing order and $A$ is positive. Clearly $V(x)$ is positive at large $x > x_3$, negative between $x_2$ and $x_3$, and so on.

Now, say I wish to evaluate

$$\int_{x_2}^{x_3}\sqrt{-V(x)}\mathrm dx$$

How do I do it?

2 Answers 2