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Question Number 74123 by liki last updated on 19/Nov/19

Commented by liki last updated on 19/Nov/19

...i need help roman (iii) plz..

$$...{i}\:{need}\:{help}\:{roman}\:\left({iii}\right)\:{plz}.. \\ $$

Commented by liki last updated on 19/Nov/19

...(iii) mr mind is power plz assist me or anyone

$$...\left({iii}\right)\:{mr}\:{mind}\:{is}\:{power}\:{plz}\:{assist}\:{me}\:{or}\:{anyone} \\ $$

Answered by ajfour last updated on 19/Nov/19

I=∫tan^(−1) ((√)(((1−sin x)/(1+sin x))))dx    =∫tan^(−1) ∣tan ((π/4)−(x/2))∣dx    = ∫((π/4)−(x/2)+nπ)dx  n  such that  0 < (π/4)−(x/2)+nπ < (π/2)  I = ((π/4)−(x/2)+nπ)x+c .

$${I}=\int\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{}\left(\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\right)\right){dx} \\ $$$$\:\:=\int\mathrm{tan}^{−\mathrm{1}} \mid\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}\right)\mid{dx} \\ $$$$\:\:=\:\int\left(\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}+{n}\pi\right){dx} \\ $$$${n}\:\:{such}\:{that}\:\:\mathrm{0}\:<\:\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}+{n}\pi\:<\:\frac{\pi}{\mathrm{2}} \\ $$$${I}\:=\:\left(\frac{\pi}{\mathrm{4}}−\frac{{x}}{\mathrm{2}}+{n}\pi\right){x}+{c}\:. \\ $$$$ \\ $$

Commented by ajfour last updated on 19/Nov/19

It should have been only the radical  sign instead of ∫ sign , because  two integrals should then  demand for two ′dx′ . As there  is only single  dx there should  be single ∫ .  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 02 marks.

$${It}\:{should}\:{have}\:{been}\:{only}\:{the}\:{radical} \\ $$$${sign}\:{instead}\:{of}\:\int\:{sign}\:,\:{because} \\ $$$${two}\:{integrals}\:{should}\:{then} \\ $$$${demand}\:{for}\:{two}\:'{dx}'\:.\:{As}\:{there} \\ $$$${is}\:{only}\:{single}\:\:{dx}\:{there}\:{should} \\ $$$${be}\:{single}\:\int\:. \\ $$$${If}\:{initially}\:\:{question}\:{was}\:{given}\: \\ $$$${by}\:{teacher}\:{handwritten}\:{on}\:{paper}, \\ $$$${the}\:{typist}\:{can}\:{take}\:{the}\:{radical} \\ $$$${to}\:{be}\:{the}\:{integral}\:{sign},\:{if}\:{the} \\ $$$${handwriting}\:{isn}'{t}\:{quite}\:{clear}. \\ $$$${plus}\:{the}\:{question}\:{is}\:{of}\:\mathrm{02}\:{marks}. \\ $$

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..

$$...{thanks}\:{sir}\:,{but}\:{why}\:{did}\:{you}\:{put}\:{that}\:{radical}\:{sign} \\ $$$${while}\:{in}\:{our}\:{question}\:{no}\:{radical}.. \\ $$

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