Question Number 74123 by liki last updated on 19/Nov/19
Commented by liki last updated on 19/Nov/19
$$…{i}\:{need}\:{help}\:{roman}\:\left({iii}\right)\:{plz}.. \\ $$
Commented by liki last updated on 19/Nov/19
$$…\left({iii}\right)\:{mr}\:{mind}\:{is}\:{power}\:{plz}\:{assist}\:{me}\:{or}\:{anyone} \\ $$
Answered by ajfour last updated on 19/Nov/19
$${I}=\int\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{}\left(\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\right)\right){dx} \\ $$$$\:\:=\int\mathrm{tan}^{−\mathrm{1}} \mid\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}\right)\mid{dx} \\ $$$$\:\:=\:\int\left(\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}+{n}\pi\right){dx} \\ $$$${n}\:\:{such}\:{that}\:\:\mathrm{0}\:<\:\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}+{n}\pi\:<\:\frac{\pi}{\mathrm{2}} \\ $$$${I}\:=\:\left(\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}+{n}\pi\right){x}+{c}\:. \\ $$$$ \\ $$
Commented by ajfour last updated on 19/Nov/19
$${It}\:{should}\:{have}\:{been}\:{only}\:{the}\:{radical} \\ $$$${sign}\:{instead}\:{of}\:\int\:{sign}\:,\:{because} \\ $$$${two}\:{integrals}\:{should}\:{then} \\ $$$${demand}\:{for}\:{two}\:'{dx}'\:.\:{As}\:{there} \\ $$$${is}\:{only}\:{single}\:\:{dx}\:{there}\:{should} \\ $$$${be}\:{single}\:\int\:. \\ $$$${If}\:{initially}\:\:{question}\:{was}\:{given}\: \\ $$$${by}\:{teacher}\:{handwritten}\:{on}\:{paper}, \\ $$$${the}\:{typist}\:{can}\:{take}\:{the}\:{radical} \\ $$$${to}\:{be}\:{the}\:{integral}\:{sign},\:{if}\:{the} \\ $$$${handwriting}\:{isn}'{t}\:{quite}\:{clear}. \\ $$$${plus}\:{the}\:{question}\:{is}\:{of}\:\mathrm{02}\:{marks}. \\ $$
Commented by liki last updated on 19/Nov/19
$$…{thanks}\:{sir}\:,{but}\:{why}\:{did}\:{you}\:{put}\:{that}\:{radical}\:{sign} \\ $$$${while}\:{in}\:{our}\:{question}\:{no}\:{radical}.. \\ $$