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Author: Tinku Tara

L-0-1-4-3x-4-5x-dx-

Question Number 208871 by Shrodinger last updated on 26/Jun/24 $${L}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}{dx} \\ $$ Answered by Sutrisno last updated on 26/Jun/24 $${misal} \\ $$$$\sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}={p}\rightarrow{x}=\frac{−\mathrm{4}{p}^{\mathrm{2}} +\mathrm{4}}{\mathrm{5}{p}^{\mathrm{2}}…

Question-208896

Question Number 208896 by efronzo1 last updated on 26/Jun/24 Answered by MM42 last updated on 27/Jun/24 $${s}_{\mathrm{1}} =\mathrm{32}−\int_{\mathrm{0}} ^{\mathrm{4}} \sqrt{\mathrm{64}−{x}^{\mathrm{2}} }{dx}\:\:\:\:\:;\:\:{x}=\mathrm{8}{sin}\theta \\ $$$$\Rightarrow=\mathrm{32}−\mathrm{64}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:{cos}^{\mathrm{2}}…

Question-208880

Question Number 208880 by efronzo1 last updated on 26/Jun/24 Answered by Frix last updated on 26/Jun/24 $${a},\:{b},\:{c}\:>\mathrm{0}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{{a}+\sqrt[{\mathrm{3}}]{\mathrm{2}}+\sqrt[{\mathrm{3}}]{\mathrm{4}}}+\sqrt[{\mathrm{3}}]{{b}}+\sqrt[{\mathrm{3}}]{{c}}>\mathrm{0} \\ $$$$\mathrm{The}\:\mathrm{question}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}. \\ $$ Terms of Service Privacy…

Question-208852

Question Number 208852 by Tawa11 last updated on 25/Jun/24 Answered by Frix last updated on 25/Jun/24 $$\mathrm{3}^{−\mathrm{3}\left({x}^{\mathrm{2}} −{x}\right)} ={x}^{\mathrm{2}} −{x}\:\Rightarrow\:{x}^{\mathrm{2}} −{x}>\mathrm{0}\:\Leftrightarrow\:{x}<\mathrm{0}\vee{x}>\mathrm{1} \\ $$$${t}={x}^{\mathrm{2}} −{x}\:\Leftrightarrow\:{x}=\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{4}{t}+\mathrm{1}}}{\mathrm{2}} \\…

Question-208855

Question Number 208855 by efronzo1 last updated on 25/Jun/24 Answered by mr W last updated on 25/Jun/24 $${let}\:{t}=\mathrm{1}+\mid{x}\mid\geqslant\mathrm{1} \\ $$$$\frac{\mathrm{2024}^{−{t}} −\lambda}{\mathrm{2024}^{−{t}} −\lambda^{−\mathrm{1}} }=\lambda\:\mathrm{2024}^{{t}} \\ $$$$\mathrm{2024}^{−{t}}…

Question-208828

Question Number 208828 by efronzo1 last updated on 24/Jun/24 Answered by mr W last updated on 24/Jun/24 $${BM}={MC}={a},\:{say} \\ $$$${AM}={DM}=\mathrm{2}{a} \\ $$$$\frac{{BM}}{\mathrm{6}}=\frac{{MQ}}{\mathrm{4}}\:\Rightarrow{MQ}=\frac{\mathrm{2}{a}}{\mathrm{3}}\:\Rightarrow{QD}=\frac{\mathrm{4}{a}}{\mathrm{3}} \\ $$$$\left(\mathrm{6}+\mathrm{4}\right)^{\mathrm{2}} ={a}^{\mathrm{2}}…

does-the-rule-of-odd-and-even-functions-can-be-applied-with-improper-integration-I-xe-x-2-dx-while-f-x-xe-x-2-is-odd-then-I-0-

Question Number 208842 by NasaSara last updated on 24/Jun/24 $${does}\:{the}\:{rule}\:{of}\:{odd}\:{and}\:{even}\:{functions}\: \\ $$$${can}\:{be}\:{applied}\:{with}\:{improper}\:{integration}? \\ $$$${I}=\int_{−\infty} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {dx}\: \\ $$$${while}\:\:{f}\left({x}\right)=\:{xe}^{−{x}^{\mathrm{2}} } \:{is}\:{odd} \\ $$$${then}\:{I}\:=\mathrm{0} \\…