This has been messing with me and I have a feeling this is relatively simple. Given this integral
$$\int_{x^2}^{\ln(x)} e^{-t^2}dt$$
What would be its domain? Would it just be the domain of ln(x)?
2026-03-26 07:58:38.1774511918
Find domain of an integral with variable bounds
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Yes, you are correct.
The graph of $e^{-x^2}$ is as follows:
This is continuous for all $x \in R$. As a result, it's integral will also be a continuous function. This means that the domain of the integral will just be the domain of $\ln x$ (since the domain of $x^2$ is $R$). Therefore, the domain of the given integral is $(0,\infty)$