I have an integral,
$$\int_{0}^{1} \int_{y}^{1} e^{x^2} dx dy$$
I tried to apply integration by parts on the inner integral with respect to $x$ but it didn't seem to progress. Does anyone have a better approach?
2026-03-25 03:20:43.1774408843
Finding value of $\int_{0}^{1} \int_{y}^{1} e^{x^2} dx dy$
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Note that, since the region of integration is the triangle whose vertices ae $(0,0)$, $(1,0)$, and $(1,1)$, your integral is equal to$$\int_0^1\int_0^xe^{x^2}\,\mathrm dy\,\mathrm dx=\int_0^1xe^{x^2}\,\mathrm dx.$$