## Thomas' Calculus 13th Edition

$2$
Consider $I= \int_0^{\sqrt {\ln 3}} \int_0^{2x} e^{x^2} dy dx$ or, $= \int_0^{\sqrt {\ln 3}} [ y e^{x^2}]_0^{2x} dy$ or, $= \int_0^{\sqrt {\ln 3}}2x e^{x^2} dy$ Set $a = x^2 \implies da=2x dx$ Now, $I=\int_0^{\ln 3} e^{a} da=[e^a]_0^{\ln 3}=3-1=2$