Question Number 191921 by Rupesh123 last updated on 03/May/23
Answered by AST last updated on 03/May/23
$$\int\left(\mathrm{3}{x}+\mathrm{5}\right){dx}=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{5}{x}+{c} \\ $$$$\int_{−\mathrm{4}} ^{\mathrm{2}} \left(\mathrm{3}{x}+\mathrm{5}\right){dx}=\left(\mathrm{16}+{c}\right)−\left(\mathrm{4}+{c}\right)=\mathrm{12} \\ $$$$\Rightarrow\left(\mathrm{4}+{log}_{\mathrm{3}} {x}\right)\left({log}_{\mathrm{3}} {x}\right)=\mathrm{12} \\ $$$$\Rightarrow\left(\mathrm{4}+{p}\right){p}=\mathrm{12}\Rightarrow{p}^{\mathrm{2}} +\mathrm{4}{p}−\mathrm{12}=\mathrm{0}\:\:\:\:\:\left({p}={log}_{\mathrm{3}} {x}\right) \\ $$$$\Rightarrow{p}=−\mathrm{6}\:{or}\:\mathrm{2} \\ $$$$\Rightarrow{x}=\mathrm{3}^{−\mathrm{6}} =\frac{\mathrm{1}}{\mathrm{729}}\:{or}\:\mathrm{9} \\ $$
Commented by Rupesh123 last updated on 04/May/23
Perfect ��