Đáp án:
$1)\quad I =\dfrac12$
$2)\quad I = 9$
Giải thích các bước giải:
$1)\quad I = \displaystyle\int\limits_1^2dy\displaystyle\int\limits_0^{\ln y}e^xdx$
$\Leftrightarrow I = \displaystyle\int\limits_1^2\left(e^x\Bigg|_0^{\ln y}\right)dy$
$\Leftrightarrow I = \displaystyle\int\limits_1^2(y - 1)dy$
$\Leftrightarrow I = \left(\dfrac{y^2}{2} - y\right)\Bigg|_1^2$
$\Leftrightarrow I = \dfrac12$
$2)\quad I = \displaystyle\int\limits_2^4dx\displaystyle\int\limits_x^{2x}\dfrac{y}{x}dy$
$\Leftrightarrow I = \displaystyle\int\limits_2^4\left(\dfrac{y^2}{2x}\Bigg|_x^{2x}\right)dx$
$\Leftrightarrow I = \displaystyle\int\limits_2^4\dfrac{3x}{2}dx$
$\Leftrightarrow I = \dfrac{3x^2}{4}\Bigg|_2^4$
$\Leftrightarrow I = 9$
