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Author: Tinku Tara

Evaluate-the-integral-R-3x-2-14xy-8y-2-dxdy-for-the-region-R-in-the-1st-quadrant-bounded-by-the-lines-y-3-2-x-1-y-3-2-x-3-y-1-4-x-and-y-1-4-x-1-

Question Number 73715 by Learner-123 last updated on 15/Nov/19 $${Evaluate}\:{the}\:{integral}\:: \\ $$$$\underset{\:\mathbb{R}} {\int}\int\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{14}{xy}+\mathrm{8}{y}^{\mathrm{2}} \right){dxdy}\:{for}\:{the}\:{region} \\ $$$$\mathbb{R}\:\mathrm{in}\:{the}\:\mathrm{1}{st}\:{quadrant}\:{bounded}\:{by}\:{the} \\ $$$${lines}\:{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{1},{y}=\frac{−\mathrm{3}}{\mathrm{2}}{x}+\mathrm{3},{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x} \\ $$$${and}\:{y}=−\frac{\mathrm{1}}{\mathrm{4}}{x}+\mathrm{1}\:. \\ $$ Commented by…

Question-73712

Question Number 73712 by FCB last updated on 15/Nov/19 Answered by MJS last updated on 15/Nov/19 $$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\:=−\infty \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{1}}{{x}}=+\infty \\ $$$$\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}}…