Question

Integration question

Answer 1

\[\int\limits_{0}^{\ln3}\int\limits_{0}^{\ln2} e^{x+y} dy dx\]

Answer 2

please you have to separate the variable, so you will calculate two integrals in one variable, namely:
\[\int\limits_{0}^{\ln3}e ^{x}dx \int\limits_{0}^{\ln2}e ^{y}dy\]

Answer 3

...

Answer 4

if \[x \in (0,\ln3), y \in(0,\ln2)\]

Answer 5

he means\[\int\limits_{0}^{\ln3}[\int\limits_{0}^{\ln2}e^{x+y}dy]dx\]

Answer 6

yes

Answer 7

now u can take out that e^{y} part when you are integrating with respect to x

Answer 8

so u'll get\[\int\limits_{0}^{\ln 3}e^x.dx[\int\limits_{0}^{\ln 2}e^y.dy]\]

Answer 9

that how its separated now u have a two parts one for x and one for y so first integrate
e^{y}.dy part

Answer 10

So when i integrate it with respect to y will it be 2 e^x?