Cho f(x) là hàm số liên tục trên [a;b] (với a<b) và F(x) là một nguyên hàm của f(x) trên [a;b] . Mệnh đề nào dưới đây đúng?

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMjhvLHfij5gC1rhimfMBNvxyNvgaCLMB0XfBP1 % wA0n3x7fwFETNy9TNzCXwzMrhkGidERmdiCjxANHgDPWfDLHhD7rwF % 41xpCXwzMrNlGyexSvMz0HciYG3kZacxYL2zOrxkGWLCPDgA0X3x7f % wFETNy9bWexLMBbXgBcf2CPn2qVrwzqf2zLnharuavP1wzZbItLDhi % s9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyai % baieYlNi-xH8yiVC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0x % bbG8FasPYRqj0-yi0dXdbba9pGe9xq-JbbG8A8frFve9Fve9Ff0dme % aabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbmaapeha % paqaa8qacaWGMbWaaeWaa8aabaWdbiaaikdacaWG4bGaey4kaSIaaG % 4maaGaayjkaiaawMcaaiaabsgacaWG4baal8aabaWdbiaadggaa8aa % baWdbiaadkgaa0Gaey4kIipakiabg2da9maaeiaapaqaa8qacaWGgb % WaaeWaa8aabaWdbiaaikdacaWG4bGaey4kaSIaaG4maaGaayjkaiaa % wMcaaaGaayjcSdWdamaaDaaaleaapeGaamyyaaWdaeaapeGaamOyaa % aaaaa!777A! \int\limits_a^b {f\left( {2x + 3} \right){\rm{d}}x} = \left. {F\left( {2x + 3} \right)} \right|_a^b\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMLhvLHfij5gC1rhimfMBNvxyNvgaCLMB0XfBP1 % wA0n3x7fwFETNy9T3AUygxSvMz0Hci4bcxYL2zOrxkCrxz4r3EK1hE % 91ZACXwzMr3wGyexSvMz0HciIbcxYL2zOrxkTyexSvMz0HciHbcxYL % 2zOrxkGWLCPDgA01fatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwB % Lnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtub % sr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0x % bba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0- % vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaa % peWaa8qCa8aabaWdbiaadUgacaGGUaGaamOzamaabmaapaqaa8qaca % WG4baacaGLOaGaayzkaaGaaeizaiaadIhaaSWdaeaapeGaamyyaaWd % aeaapeGaamOyaaqdcqGHRiI8aOGaeyypa0Jaam4Aamaadmaapaqaa8 % qacaWGgbWaaeWaa8aabaWdbiaadkgaaiaawIcacaGLPaaacqGHsisl % caWGgbWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaaaiaawUfaca % GLDbaaaaa!7A03! \int\limits_a^b {k.f\left( x \right){\rm{d}}x} = k\left[ {F\left( b \right) - F\left( a \right)} \right]\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMDgvLHfij5gC1rhimfMBNvxyNvgaCLMB0XfBP1 % wA0n3x7jwFETxy9TNzCXwzMrhkGGhiCjxANHgDPWfDLHhD7rwF41xp % gXfBLzgDOaIyGWLCPDgA0LslgXfBLzgDOasyGWLCPDgA0LcatCvAUf % eBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxB % I9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8 % YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY-biLkVcLq-J % Hqpepeea0-as0Fb9pgeaYRXxe9vr0-vr0-vqpWqaaeaabiGaciaaca % qabeaadaqaaqaaaOqaaabaaaaaaaaapeWaa8qCa8aabaWdbiaadAga % daqadaWdaeaapeGaamiEaaGaayjkaiaawMcaaiaabsgacaWG4baal8 % aabaWdbiaadkgaa8aabaWdbiaadggaa0Gaey4kIipakiabg2da9iaa % dAeadaqadaWdaeaapeGaamOyaaGaayjkaiaawMcaaiabgkHiTiaadA % eadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaaaa!6ED1! \int\limits_b^a {f\left( x \right){\rm{d}}x} = F\left( b \right) - F\left( a \right)\)

D. Diện tích S của hình phẳng giới hạn bởi hai đường thẳng x= a, x = b đồ thị hàm số y= f(x) và trục hoành được tính theo công thức S = F(a) - F(b)

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Môn: Toán Lớp 12

Chủ đề: Nguyên Hàm - Tích Phân Và Ứng Dụng

Bài: Nguyên hàm

Lời giải:

Báo sai

Ta có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb % a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr % 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape % Waa8qCa8aabaWdbiaadAgadaqadaWdaeaapeGaamiEaaGaayjkaiaa % wMcaaiaabsgacaWG4baal8aabaWdbiaadkgaa8aabaWdbiaadggaa0 % Gaey4kIipakiabg2da9iabgkHiTmaadmaapaqaa8qacaWGgbGaaiik % aiaadkgacaGGPaGaeyOeI0IaamOramaabmaapaqaa8qacaWGHbaaca % GLOaGaayzkaaaacaGLBbGaayzxaaGaeyO0H4Taamiraaaa!4E95! \int\limits_b^a {f\left( x \right){\rm{d}}x} = - \left[ {F(b) - F\left( a \right)} \right] \Rightarrow D\) sai.

Diện tích \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMrfvLHfij5gC1rhimfMBNvxyNvgat1dxP5gDCX % wATLgDZ91EH1Nx7jwF7XfBLzgD8bIzCXwzMrhkGGhiCjxANHgDPacx % YL2zOrhFCrxz4r3EK1hE9bWexLMBbXgBcf2CPn2qVrwzqf2zLnharu % avP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqe % e0evGueE0jxyaibaieYlNi-xH8yiVC0xbbL8F4rqqrFfpeea0xe9Lq % -Jc9vqaqpepm0xbbG8FasPYRqj0-yi0dXdbba9pGe9xq-JbbG8A8fr % Fve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaa % aaaaWdbiaadofacqGH9aqpdaWdXbWdaeaapeWaaqWaa8aabaWdbiaa % dAgadaqadaWdaeaapeGaamiEaaGaayjkaiaawMcaaaGaay5bSlaawI % a7aiaabsgacaWG4baal8aabaWdbiaadggaa8aabaWdbiaadkgaa0Ga % ey4kIipaaaa!6599! S = \int\limits_a^b {\left| {f\left( x \right)} \right|{\rm{d}}x} \)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMfcvLHfij5gC1rhimfMBNvxyNvgaCjvANHgDHj % NCVDhidbWexLMBbXgBcf2CPn2qVrwzqf2zLnharuavP1wzZbItLDhi % s9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyai % baieYlNi-xH8yiVC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0x % bbG8FasPYRqj0-yi0dXdbba9pGe9xq-JbbG8A8frFve9Fve9Ff0dme % aabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaaWdbiabgkDi % Elaadoeaaaa!4522! \Rightarrow C\) sai.

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaM1hvLHfij5gC1rhimfMBNvxyNvgaCLMB0XfBP1 % wA0n3x7fwFETNy9TNzCXwzMrhkGidERmdiCjxANHgDPWfDLHhD7rwF % 41xpCzMCHn2EX03EY0hxSvMz05cigXfBLzgDOaIm4TYmGWLCPDgA0L % ciCjxANHgD891EH1Nx7jwFamXvP5wqSXMqHnxAJn0BKvguHDwzZbqe % fqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2Dae % bbnrfifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj % 0-OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr % 0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaa % aaaaa8qadaWdXbWdaeaapeGaamOzamaabmaapaqaa8qacaaIYaGaam % iEaiabgUcaRiaaiodaaiaawIcacaGLPaaacaqGKbGaamiEaaWcpaqa % a8qacaWGHbaapaqaa8qacaWGIbaaniabgUIiYdGccqGH9aqpdaWcaa % WdaeaapeGaaGymaaWdaeaapeGaaGOmaaaadaabcaWdaeaapeGaamOr % amaabmaapaqaa8qacaaIYaGaamiEaiabgUcaRiaaiodaaiaawIcaca % GLPaaaaiaawIa7a8aadaqhaaWcbaWdbiaadggaa8aabaWdbiaadkga % aaaaaa!7D95! \int\limits_a^b {f\left( {2x + 3} \right){\rm{d}}x} = \frac{1}{2}\left. {F\left( {2x + 3} \right)} \right|_a^b\) nên A sai.

Theo tính chất của tích phân \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMLhvLHfij5gC1rhimfMBNvxyNvgaCLMB0XfBP1 % wA0n3x7fwFETNy9T3AUygxSvMz0Hci4bcxYL2zOrxkCrxz4r3EK1hE % 91ZACXwzMr3wGyexSvMz0HciIbcxYL2zOrxkTyexSvMz0HciHbcxYL % 2zOrxkGWLCPDgA01fatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwB % Lnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtub % sr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0x % bba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0- % vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaa % peWaa8qCa8aabaWdbiaadUgacaGGUaGaamOzamaabmaapaqaa8qaca % WG4baacaGLOaGaayzkaaGaaeizaiaadIhaaSWdaeaapeGaamyyaaWd % aeaapeGaamOyaaqdcqGHRiI8aOGaeyypa0Jaam4Aamaadmaapaqaa8 % qacaWGgbWaaeWaa8aabaWdbiaadkgaaiaawIcacaGLPaaacqGHsisl % caWGgbWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaaaiaawUfaca % GLDbaaaaa!7A03! \int\limits_a^b {k.f\left( x \right){\rm{d}}x} = k\left[ {F\left( b \right) - F\left( a \right)} \right]\) ; B đúng.