Question Number 94356 by ar247 last updated on 18/May/20 | ||
$$\int_{{y}} ^{\mathrm{3}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)=\mathrm{40} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{y}=? \\ $$ | ||
Commented by ar247 last updated on 18/May/20 | ||
$${help} \\ $$ | ||
Commented by MJS last updated on 18/May/20 | ||
$$\mathrm{integrate}\:\mathrm{and}\:\mathrm{then}\:\mathrm{solve}\:\mathrm{for}\:{y} \\ $$$$\left[{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}\right]_{{y}} ^{\mathrm{3}} =−{y}^{\mathrm{3}} +{y}^{\mathrm{2}} −\mathrm{2}{y}+\mathrm{24} \\ $$$$\Rightarrow \\ $$$${y}^{\mathrm{3}} −{y}^{\mathrm{2}} +\mathrm{2}{y}+\mathrm{16}=\mathrm{0} \\ $$$$\left({y}+\mathrm{2}\right)\left({y}^{\mathrm{2}} −\mathrm{3}{y}+\mathrm{8}\right)=\mathrm{0} \\ $$$$\Rightarrow\:{y}=−\mathrm{2} \\ $$ | ||