Question

evaluate int_(0--> 2) int_(0--> sqrt(y)) x e^y dxdy
step by step, please

Answer 1

need help

Answer 2

hmm...
\[\huge \int\limits_{0}^2\int\limits_{0}^\sqrt yxe^y \ dxdy\]

Answer 3

Okay, so, first thing you do is integrate this part...\[\huge \int\limits_{0}^2\color{red}{\int\limits_{0}^\sqrt yxe^y \ dx}dy\]pretending y is just a constant.

Answer 4

= int. x^2/2 * e^y dy

Answer 5

Hold on there...
\[\huge \int\limits_{0}^{\sqrt y}xe^y dx=\left.\frac{x^2e^y}{2}\right]_0^{\sqrt y} \]

Answer 6

int. x^2/2*e^y ( replace by limits) dy ,sorry

Answer 7

yes

Answer 8

Okay, so can you evaluate this part first...\[\huge \int\limits_{0}^{\sqrt y}xe^y dx=\color{blue}{\left.\frac{x^2e^y}{2}\right]_0^{\sqrt y}}\]

Answer 9

wate im lost now

Answer 10

= (y e^y)/2