Diện tích hình phẳng giới hạn bởi đồ thị hàm số bậc ba y = f(x) và các trục tọa độ là S = 32 (hình vẽ bên). Tính thể tích vật tròn xoay được tạo thành khi quay hình phẳng trên quanh trục Ox.

A. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIZaGaaG4maiaaikdacaaI4aGaeqiWdahabaGaaG4maiaaiwdaaaaa % aa!3C34! \frac{{3328\pi }}{{35}}\)

B. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aI5aGaaGOmaiaaigdacaaI2aGaeqiWdahabaGaaGynaaaaaaa!3B79! \frac{{9216\pi }}{5}\)

C. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaGaaG4maiaaiodacaaIXaGaaGOmaiabec8aWbqaaiaaiodacaaI % 1aaaaaaa!3CE8! \frac{{13312\pi }}{{35}}\)

D. \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaGaaGimaiaaikdacaaI0aGaeqiWdahabaGaaGynaaaaaaa!3B6E! \frac{{1024\pi }}{5}\)

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Chủ đề: Đề thi THPT QG

Môn: Toán

Lời giải:

Báo sai

Dựa vào đồ thị hàm số ta suy ra \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamiEaaGaayjkaiaawMcaaiabg2da9iaadUgadaqadaqaaiaa % dIhacqGHsislcaaIXaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYa % aaaOWaaeWaaeaacaWG4bGaeyOeI0IaaGinaaGaayjkaiaawMcaaaaa % !44AC! f\left( x \right) = k{\left( {x - 1} \right)^2}\left( {x - 4} \right)\) (với k > 0)

Mặt khác \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiabg2 % da9maapehabaWaaqWaaeaacaWGRbWaaeWaaeaacaWG4bGaeyOeI0Ia % aGymaaGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaakmaabmaaba % GaamiEaiabgkHiTiaaisdaaiaawIcacaGLPaaaaiaawEa7caGLiWoa % caWGKbGaamiEaaWcbaGaaGimaaqaaiaaisdaa0Gaey4kIipakiabg2 % da9iaaiodacaaIYaGaeyi1HSTaam4Aaiabg2da9maalaaabaGaaG4m % aiaaikdaaeaadaWdXbqaamaaemaabaWaaeWaaeaacaWG4bGaeyOeI0 % IaaGymaaGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaakmaabmaa % baGaamiEaiabgkHiTiaaisdaaiaawIcacaGLPaaaaiaawEa7caGLiW % oacaWGKbGaamiEaaWcbaGaaGimaaqaaiaaisdaa0Gaey4kIipaaaGc % cqGH9aqpcaaI0aaaaa!6769! S = \int\limits_0^4 {\left| {k{{\left( {x - 1} \right)}^2}\left( {x - 4} \right)} \right|dx} = 32 \Leftrightarrow k = \frac{{32}}{{\int\limits_0^4 {\left| {{{\left( {x - 1} \right)}^2}\left( {x - 4} \right)} \right|dx} }} = 4\).

Suy ra \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamiEaaGaayjkaiaawMcaaiabg2da9iaaisdadaqadaqaaiaa % dIhacqGHsislcaaIXaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYa % aaaOWaaeWaaeaacaWG4bGaeyOeI0IaaGinaaGaayjkaiaawMcaaiab % gkDiElaadAfacqGH9aqpdaWdXbqaaiaadAgadaahaaWcbeqaaiaaik % daaaGcdaqadaqaaiaadIhaaiaawIcacaGLPaaacaWGKbGaamiEaaWc % baGaaGimaaqaaiaaisdaa0Gaey4kIipakiabg2da9maapehabaWaam % WaaeaacaaI0aWaaeWaaeaacaWG4bGaeyOeI0IaaGymaaGaayjkaiaa % wMcaamaaCaaaleqabaGaaGOmaaaakmaabmaabaGaamiEaiabgkHiTi % aaisdaaiaawIcacaGLPaaaaiaawUfacaGLDbaadaahaaWcbeqaaiaa % ikdaaaGccaWGKbGaamiEaaWcbaGaaGimaaqaaiaaisdaa0Gaey4kIi % pakiabg2da9maalaaabaGaaGymaiaaiodacaaIZaGaaGymaiaaikda % cqaHapaCaeaacaaIZaGaaGynaaaaaaa!6EB4! f\left( x \right) = 4{\left( {x - 1} \right)^2}\left( {x - 4} \right) \Rightarrow V = \int\limits_0^4 {{f^2}\left( x \right)dx} = \int\limits_0^4 {{{\left[ {4{{\left( {x - 1} \right)}^2}\left( {x - 4} \right)} \right]}^2}dx} = \frac{{13312\pi }}{{35}}\).

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