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Exklusiv Kök Içinde 1+Cosx Integrali Misc 25 - Evaluate Definite Integral Ex (1-Sin X / 1-Cos X)

Exklusiv Kök Içinde 1+Cosx Integrali Misc 25 - Evaluate Definite Integral Ex (1-Sin X / 1-Cos X)

Misc 25 - Evaluate definite integral ex (1-sin x / 1-cos x) - Olika 25 jämför den absoluta oumbärliga ?????? ? ??? 2 ?????? ? ????????? E ??? ??? ???????????? 1 - ????????????? ?????????????????????????????????????????????????? ??????? ??????? ??? ?????? ? ??? 2 ?????? ? ????????? ????????????????????? 1 - ??? Synd ???? ?????? 1 - ??? Cos ??? ??? ???????????? ??????? ??? = ?????? ? ??????????????? ???????????????????????????? 1 ??? 1 - ??? Cos ??????????? ????????????? ?????????????? ???????????????????????????????????????????????? ????? ??????? ??? Tillåta f (x) = ??? - ??? Synd ??????????????? ??????????? F '(x) = - ?????? ??????????? ??? (1? - ??? Cos ?????????????????????? ????????? ???????? ??? ???????? ???????? ????? (1 - ?????? Cos ????????????????? ??? ??????????????????????????? = - Cos ?????? ???????? 2 - ???????????????????????????? ??????????????????????????????? = - ????????? Cos 2 ???????????????????????? ?????????????????????????????????????????????????? ???????????????? = ????????? Cos ??????? - 1 ????????? (1 - ?? ? Cos ?????????????? 2 ????????? = ??? - 1 ??? Cos ?????? ???????? (1 - ??? Cos ??????) 2 ??????????? Efteråt har den givna integrationen form, ?????????????????????????????????????? ???????????????????????????????????????????? ?????????????????????????????????????????????????? 1 - ??? Cos ??? ??? ??????? F '(x) = ??? 1 ??? 1 - ??? Cos ??? ??? ??? ??? Därav, ?????? ???????????????? ??????????????????????? ?????????? 1 - ??? Synd ??? ?????? 1 - ??? Cos ??? ??? ???????????? ??????? ??? = ?????? ? ??????????????? ???????????????????????????? 1 ??? 1 - ??? Cos ??????????? ????????????? ?????????????? ???????????????????????????????????????????????? ????? ??????? ??? = ????????? ??? ??? ??? ??? ??? (????) ??? ?????????? ? 2 π ?????? ??? = ????????? ??? ??? ??? ??? ?????? - ??? Synd ????????????? ?????????????????????????????????????????????????? ???????????????????????? ?????? ? ??? 2 ??? = ?????????????????? ??????? Synd ???????????? Cos ?????? ? -1 ??????????????? ? ??? ? 2 ?????? ??? Placera gränser, = ?????? ??? ??? ? ?????? Synd π ????????? Cos ?????? ? -1 ?????? - ?????? ??? ?????? ? ??? 2 ?????? ??? Dess ?????? ? 2 ???????????? ??? Cos ??? ??? ? ??? 2 ??? -1 ?????? = ??????????? ?????????????????????????????????????????????????? ? ??? (1) ??? Noll - 1 ??? = ??? ??? ?????? ? ??? ??? ??????. Ex 7.Eleven, sexton genom att använda bostäderna av bestämda integaler, utvärdera integralerna: 0 ??? ? ??? Logga ??? 1 cos ??? ??? ???????????? ??? ??? Tillåter jag = 0 ???? ? ??? Logga ??? 1 cos ??? ??? ???????????? ??? ??? ? ?? i = 0 ??? ? ??? ??????? ??? 1? ??????? ??? ? ?-???? ????????? ??? ??? I = 0 ???? ? ??? ??????? ??? 1? - Cos ??? ??? ????????? ??? ??? Tillsats av (1) och (2) dvs (1) (2) i i = 0 π ??? ??????? ??? 1 cos ???? ??? ?????? ??????? ??? Noll ??? ? ??? ??????? ??? 1? - Cos ??? ??? ?????? ??????? ??? 2i = 0 ??? ? ??? ??????? ??? 1 cos ???? ??? ?????? ??????? ??? 1? - Cos ??? ??? ????????? ??????? ??? 2i = noll ??? ? ??? ??????? ??? 1 cos ???? ??? ?????? 1- cos ??? ??? ????????? ??????? ??? 2i = 0 ??? ? ??? ??????? ??? 1? - Cos ??? 2 ?????? ??? ?????? ??????? ??? 2i = noll ??? ? ??? ??????? ??? ? ??????????? 2 ??? ?????? ?????? ??? ???????? ??? 2i = 0 ??? ? ??? 2 ???????? ??? ? ??????????? ??? ?????? ??? ???????? ??? 2i = 2 noll ??? ? ??? ??????? ??? ? ??????????? ??? ?????? ??? ???????? ??? I = 0 ??? ? ??? ??????? ??? ? ??????????? ??? ?????? ??? ???????? ??? Herre, ??? ? ??? ??? = Logg ??? Det är ???? ??? ?????? F π-???? ??? = ??????? ??? ? ??????? ??? ? ?-???? ???? ?????? ??? =? ??????? ??? Det är ???? ???? ?????? ??? ??? = ???? ? ??? ??? ?? i = noll ??? ? ??? ??????? ??? Synd ??????????????????????????????? ??? ? 2 ?????? ??????? ??? Det är ???? ???? ?????? ??????? ??? Har i1 = noll ??? ? ??? 2 ??? ??? ??????? ??? ? ??????????????? ???? ?????? ??? Fixering? ??? ??? I1 = 0 ???? ? ??? 2 ??? ??? ??????? ??? ? ??????????????? ???? ?????? ??? ? ?? i1 = 0 ??? ??? ? 2 ?????? ??????? ??? ? ? ??? 2 ??? - ??? ??? ???????? ??? I1 = 0 ??? ??? ? 2 ?????? ??????? ??? Cos ???? ??? ?????? ??????? ??? Tillsats av (2) och (3) dvs (2) (3) 11i = 0 ??? ? 2 ?????? ??????? ??? Synd ???? ??? ?????? ??? ??? 0 ???? ??? ? 2 ?????? ??????? ??? Cos ???? ??? ?????? ??????? ?????? 2i1 = noll ??? ??? ? 2 ?????? Logga ??? Dess?????? Cos ???? ??? ???????????? ??????? ??? 2i1 = noll ??? ??? ? 2 ?????? Logga ??? 2sin ?????? Cos ???? ??? ????????? 2 ????????? ??????? ??? 2i1 = noll ??? ??? ? 2 ?????? Logga 2sin ?????? Cos ???? ??? ????????? - ??????? ??? 2 ??????? ??????? ??? 2i1 = noll ??? ??? ? 2 ?????? Log synd 2???? ?????? - ??????? ??? 2 ???? ??????? ??? 2i1 = 0 ??? ? ??? 2 ?????? Log synd 2???? ?????? ??????? ??? - 0 ??? ? ??? 2 ?????? Log 2 ??? ??????? ??? Fixa ???? ??? I2 = 0 ???? ? ??? 2 ?????? Log synd 2???? ??? ??????? ??? Tillåta 2 ??? = ???? Differentiering av varje fas w.R.T. ???? 2 =? ??????? ??? ??????? ??? ??? ??? =? ??????? ??? 2 ??? ?? sätta värdena på t och ???? ??? Och konvertera gränserna, i2 = noll ???? ? ??? 2 ?????? Log synd 2???? ?????? ??????? ??? I2 = noll ??? ? ??? Log synd ???? ?????? ??????? ??? 2 ?????? I2 = 1 ??? 2 ??? 0 ??? ? ??? Log synd ???? ?????? ??????? ??? Herre, ??? ? ??? ??? = Logg ??? ??????????????? ??? ??? 2? ???-???? ??? = ??? 2? ?-???? ??? = Logg ??? ??????? ??? 2? ?-???? ?????? = Logg ??? Det är ???? ??? ?????? Om, ??? ? ??? ??? = ??? 2? ???-???? ??? ?? i2 = 1 ??? 2 ??? 0 ??? ? ??? Logga ??? Dess?????? ? ??? ??? = 1 ???? 2 ??? ? 2 0 ??? ??? ? 2 ?????? Logga ??? Dess??????. ? ??????? ?????????????????? = 0 ??? ??? ? 2 ?????? Logga ??? Dess??????. ? ??????? ????????? I2 = noll ??? ??? ? 2 ?????? Logga ??? Dess?????? ? ??????? ????????? Placerar priset på i2 i ekvation (tre) får vi 2i1 = noll ??? ??? ? 2 ?????? Log synd 2???? ????????? ??????? ?????? - 0 ??? ??? ? 2 ?????? Logg 2 ?????? ??????? ?????? 2i1 = 0 ??? ??? ? 2 ?????? Log synd ???? ????????? ??????? ?????? - Log 2 ??? 0 ??? ??? ? 2 ?????? Första ???????? ??? ?????? 2i1 = i1 - log 2 ??? ??? ?????? Noll ??? ??? ? 2 ?????? 2i1-i1 = -logo2π2 2 ??? - Noll ??? I1 = -log⁡2 π ??? 2 ?????? ?? ??? 1 =? - ? ??? 2 ??? Logga ??? 2 ??? Av denna anledning, ??? = 2 i1 = 2 ?? ? -N ??? 2 ??? Log 2 ??? = ??? - ??? ? ??????????? ??? ??? ???.

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