Cho hàm số y = f(x) với f(0) = f(1) = 1. Biết rằng:\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaaca % WGLbWaaWbaaSqabeaacaWG4baaaOWaamWaaeaacaWGMbWaaeWaaeaa % caWG4baacaGLOaGaayzkaaGaey4kaSIabmOzayaafaWaaeWaaeaaca % WG4baacaGLOaGaayzkaaaacaGLBbGaayzxaaGaaeizaiaadIhaaSqa % aiaaicdaaeaacaaIXaaaniabgUIiYdGccqGH9aqpcaWGHbGaamyzai % abgUcaRiaadkgaaaa!4C3F! \int\limits_0^1 {{e^x}\left[ {f\left( x \right) + f'\left( x \right)} \right]{\rm{d}}x} = ae + b\)  Tính \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuaiabg2 % da9iaadggadaahaaWcbeqaaiaaikdacaaIWaGaaGymaiaaiEdaaaGc % cqGHRaWkcaWGIbWaaWbaaSqabeaacaaIYaGaaGimaiaaigdacaaI3a % aaaaaa!40C7! Q = {a^{2017}} + {b^{2017}}\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe % qaaiaadwhacqGH9aqpcaWGMbWaaeWaaeaacaWG4baacaGLOaGaayzk % aaaabaGaaeizaiaadAhacqGH9aqpcaWGLbWaaWbaaSqabeaacaWG4b % aaaOGaaeizaiaadIhaaaGaay5EaaGaeyO0H49aaiqaaqaabeqaaiaa % bsgacaWG1bGaeyypa0JabmOzayaafaWaaeWaaeaacaWG4baacaGLOa % GaayzkaaGaaeizaiaadIhaaeaacaWG2bGaeyypa0JaamyzamaaCaaa % leqabaGaamiEaaaaaaGccaGL7baaaaa!5355! \left\{ \begin{array}{l} u = f\left( x \right)\\ {\rm{d}}v = {e^x}{\rm{d}}x \end{array} \right. \Rightarrow \left\{ \begin{array}{l} {\rm{d}}u = f'\left( x \right){\rm{d}}x\\ v = {e^x} \end{array} \right.\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaaca % WGLbWaaWbaaSqabeaacaWG4baaaOWaamWaaeaacaWGMbWaaeWaaeaa % caWG4baacaGLOaGaayzkaaGaey4kaSIabmOzayaafaWaaeWaaeaaca % WG4baacaGLOaGaayzkaaaacaGLBbGaayzxaaGaaeizaiaadIhaaSqa % aiaaicdaaeaacaaIXaaaniabgUIiYdGccqGH9aqpdaabcaqaaiaadw % gadaahaaWcbeqaaiaadIhaaaGccaWGMbWaaeWaaeaacaWG4baacaGL % OaGaayzkaaaacaGLiWoadaqhaaWcbaGaaGymaaqaaiaaikdaaaGccq % GHsisldaWdXbqaaiaadwgadaahaaWcbeqaaiaadIhaaaGcceWGMbGb % auaadaqadaqaaiaadIhaaiaawIcacaGLPaaacaqGKbGaamiEaaWcba % GaaGimaaqaaiaaigdaa0Gaey4kIipakiabgUcaRmaapehabaGaamyz % amaaCaaaleqabaGaamiEaaaakiqadAgagaqbamaabmaabaGaamiEaa % GaayjkaiaawMcaaiaabsgacaWG4baaleaacaaIWaaabaGaaGymaaqd % cqGHRiI8aOGabmywayaaraaaaa!6B0B! \int\limits_0^1 {{e^x}\left[ {f\left( x \right) + f'\left( x \right)} \right]{\rm{d}}x} = \left. {{e^x}f\left( x \right)} \right|_1^2 - \int\limits_0^1 {{e^x}f'\left( x \right){\rm{d}}x} + \int\limits_0^1 {{e^x}f'\left( x \right){\rm{d}}x} \bar Y\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaam % yzaiaadAgadaqadaqaaiaaigdaaiaawIcacaGLPaaacqGHsislcaWG % MbWaaeWaaeaacaaIWaaacaGLOaGaayzkaaaaaa!3F2D! = ef\left( 1 \right) - f\left( 0 \right)\) = e - 1

Do đó a= 1; b = -1

Suy ra \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuaiabg2 % da9iaadggadaahaaWcbeqaaiaaikdacaaIWaGaaGymaiaaiEdaaaGc % cqGHRaWkcaWGIbWaaWbaaSqabeaacaaIYaGaaGimaiaaigdacaaI3a % aaaaaa!40C7! Q = {a^{2017}} + {b^{2017}}\) = 0