Question

integral from o to 2, of the integral from y to 2y of (4x-y)dxdy

Answer 1

\[\int\limits_{0}^{2}\int\limits_{y^2}^{2y}4x-ydxdy\]

Answer 2

\[\large \int\limits_{0}^{2}\int\limits_{y^2}^{2y}4x-ydxdy\]


\[\large \int\limits_{0}^{2}\left. 2x^2-yx \right|_{y^2}^{2y}dy\]


\[\large \int\limits_{0}^{2}(2(2y)^2-y(2y))-(2(y^2)^2-y(y^2))dy\]


\[\large \int\limits_{0}^{2}8y^2-2y^2-2y^4+y^3dy\]


\[\large \int\limits_{0}^{2}-2y^4+y^3+6y^2dy\]


\[\large \left. -\frac{2}{5}y^5+\frac{1}{4}y^4+2y^3 \right|_{0}^{2}\]


\[\large \left(-\frac{2}{5}(2)^5+\frac{1}{4}(2)^4+2(2)^3\right)-\left(-\frac{2}{5}(0)^5+\frac{1}{4}(0)^4+2(0)^3\right)\]


\[\large \frac{36}{5}-0\]


\[\large \frac{36}{5}\]


So \[\large \int\limits_{0}^{2}\int\limits_{y^2}^{2y}4x-ydxdy=\frac{36}{5}\]

Answer 3

you're my hero, thank you soo much! i was just making simple errors here and there -_-"