Chapter 15: Multiple Integrals - Section 15.2 - Double Integrals over General Regions - Exercises 15.2 - Page 883: 51

$2$

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, $I=\int_0^{\ln 3} e^{a} da=[e^a]_0^{\ln 3}=3-1=2$