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Class xii ncert maths chapter 07 integrals 7integrals

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Class XIINCERTMathsChapter-07 - Integrals7.Integrals 222020114sec334 1tan3xIxdxx 222022sec... 16314tanxIdxx Consider,22202sec14tanxdxxLet 2 tanx = t2sec2xdx = dtWhen x = 0, t = 0 and when x =2, t =222200102sec14tan1tanxdtdxxtt 11tantan02 Therefore, from (1), we obtain2632366I Question 28:36sincossin2xxdxxSolution 28:Let36sincossin2xxIdxx36sincossin2xxIdxx 36sincos1 12sincosxxIdxx   3226sincos1sincos2sincosxxIdxxxxx326sincos1sincosLet sincossincosxx dxIxxxxtxx dxdt151
Class XIINCERTMathsChapter-07 - Integrals7.Integrals3 1213221331when,and when x =,62321xttdtIt3 1213221dtIt222a-a0111As, therefore,is an even function.1112atttfx dxfx dx It is known that if f(x) is an even function, then3 12203 1120212sindtItt1312sin2= 2(π/12) = π/6Question 29:101dxxxSolution 29:Let101dxIxx101111xxIdxxxxx101100111xxdxxxxdxxdx  1123320023221332221133xx    23223152
Class XIINCERTMathsChapter-07 - Integrals7.Integrals2.2234 23Question 30:40sincos916sin2xxdxxSolution 30:Let I =40sincos916sin2xxdxxAlso let sin xcos x = t(cos x + sinx) dx = dtWhen x = 0, t = - 1 and when x =4, t = 022222sincossincos2sincosxxtxxt221sin2sin21xtxt  021021916 191616dtItdtt  0022211012516541154log42 554dtdttttt 11log 1log4091log940Question 31:120sin2 tansinxx dxSolution 31:Let112200sin2 tansin2sincostansinIxx dxxxx dx153
Class XIINCERTMathsChapter-07 - Integrals7.IntegralsAlso, let sin x = tcos x dx = dtWhen x = 0, t = 0 and when x =2, t = 11102tan( )Itt dt… (1)Consider111.tantan.tandttdtttdtttdtdtdt221221221tan..212tan111221tttdtttttdtt 21221112111100tan1111.2221tan11.tan222tan1.tantan222ttdtdtttttttttttdtt11244 1112242From equation (1), we obtain121422IQuestion 32:0tansectanxxdxxxSolution 32:Let 0tan... 1sectanxxdxxx 000tansectanaaxxIdxfx dxfax dxxx0tansectanxxIdxxx 0tan... 2sectanxxIdxxxAdding (1) and (2), we obtain154
Class XIINCERTMathsChapter-07 - Integrals7.Integrals0tan2sectanxIdxxx0sincos21sincoscosxxIdxxxx000sin1121sin121.1sinxIdxxIdxdxx  2002201sin2cos2sectansecxIxdxxIxxx dx2022tansec2tansectan0sec0IxxI222010122II 2222II Question 33:41123xxxdxSolution 33:LetI=41123xxxdx444111123Ixdxxdxxdx 123... 1IIII444123111411where,1,2,311014Ixdx Ixdx and IxdxIxdxxforx4114211(1)2IxdxxIx155

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Derivative, Logarithm, constant term, function sin 2x

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