B\u00e0i t\u1eadp (trang 175-176-177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao)<\/h2>\n

B\u00e0i 41 (trang 175 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ecm nguy\u00ean h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau:<\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/div>\n

<\/p>\n

Ch\u00fa \u00fd: ta c\u00f3 th\u1ec3 t\u00ecm nguy\u00ean h\u00e0m n\u00e0y theo c\u00e1ch kh\u00f4ng \u0111\u01b0a ra bi\u1ebfn u nh\u01b0 sau:<\/p>\n

<\/p>\n

<\/p>\n

B\u00e0i 42 (trang 175 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ecm nguy\u00ean h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau:<\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

B\u00e0i 43 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ecm nguy\u00ean h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau:<\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

B\u00e0i 44 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ecm h\u00e0m s\u1ed1 y = f(x) n\u1ebfu bi\u1ebft dy = 12x(3x^{2<\/sup>-1)3<\/sup>\u00a0dx v\u00e0 f(1) = 3<\/p>\n}

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

Theo \u0111\u1ecbnh ngh\u0129a nguy\u00ean h\u00e0m th\u00ec f(x) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a h\u00e0m g(x) = 12x(3x^{2<\/sup>-1)3<\/sup><\/p>\n}

<\/p>\n

B\u00e0i 45 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

X\u00e1c \u0111\u1ecbnh s\u1ed1 b d\u01b0\u01a1ng \u0111\u1ec3 t\u00edch ph\u00e2n c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t.:<\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

T\u1eeb b\u1ea3ng bi\u1ebfn thi\u00ean ta th\u1ea5y y l\u1edbn nh\u1ea5t b\u1eb1ng 1\/6 khi x = 1<\/p>\n

V\u1eady \u0111\u1ec3 t\u00edch ph\u00e2n I c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t khi b = 1.<\/p>\n

B\u00e0i 46 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

Cho bi\u1ebft :<\/p>\n

<\/p>\n

H\u00e3y t\u00ecm:<\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1edf b\u1ea3n c\u1ee7a nguy\u00ean h\u00e0m ta c\u00f3:<\/p>\n

<\/p>\n

B\u00e0i 47 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

Cho h\u00e0m s\u1ed1 f(x) li\u00ean t\u1ee5c tr\u00ean [a; b]<\/p>\n

<\/p>\n

\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a h\u00e0m s\u1ed1 f(x) tr\u00ean [a; b] v\u00e0 \u0111\u01b0\u1ee3c k\u00ed hi\u1ec7u m(f). ch\u1ee9ng minh r\u1eb1ng t\u1ed3n t\u1ea1i \u0111i\u1ec3m c \u2208(a;b) sao cho m(f) = f(c).<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

G\u1ecdi F(x) l\u00e0 m\u1ed9t nguy\u00ean h\u00e0m c\u1ee7a f(x) => F\u2019(x) = f(x) =>F(x) li\u00ean t\u1ee5c tr\u00ean [a; b] c\u00f3 \u0111\u1ea1o h\u00e0m tr\u00ean (a; b) v\u00e0 th\u1ecfa m\u00e3n :<\/p>\n

<\/p>\n

Theo \u0111\u1ecbnh l\u00fd Lagr\u0103ng th\u00ec \u2203c \u2208(a;b) sao cho<\/p>\n

<\/p>\n

V\u00ec F’ (c)=f(c)=> \u2203c \u2208(a;b) \u0111\u1ec3 m(f) = f(c) (\u0111pcm)<\/p>\n

B\u00e0i 48 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

Gi\u1ea3 s\u1eed m\u1ed9t v\u1eadt t\u1eeb tr\u1ea1ng th\u00e1i ngh\u1ec9 khi t = 0 (s) chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng v\u1edbi v\u1eadn t\u1ed1c v(t) = t(5 \u2013 t) (m\/s). t\u00ecm qu\u1ea3ng \u0111\u01b0\u1eddng v\u1eadt \u0111i \u0111\u01b0\u1ee3c cho t\u1edbi khi n\u00f3 d\u1eebng l\u1ea1i.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

Khi v\u1eadt d\u1eebng l\u1ea1i ngh\u0129a l\u00e0:<\/p>\n

<\/p>\n

=> sau 5 gi\u00e2y th\u00ec v\u1eadt d\u1eebng l\u1ea1i. V\u1eady qu\u00e3ng \u0111\u01b0\u1eddng v\u1eadt \u0111i \u0111\u01b0\u1ee3c l\u00e0:<\/p>\n

<\/p>\n

B\u00e0i 49 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

M\u1ed9t ch\u1ea5t \u0111i\u1ec3m A t\u1eeb tr\u1ea1ng th\u00e1i ngh\u1ec9 chuy\u1ec3n \u0111\u1ed9ng v\u1edbi v\u1eadn t\u1ed1c nhanh d\u1ea7n \u0111\u1ec1u. 8 gi\u00e2y sau \u0111\u1ea1t \u0111\u1ebfn v\u1eadn t\u1ed1c 6 m\/s. t\u1eeb th\u1eddi \u0111i\u1ec3m \u0111\u00f3 n\u00f3 chuy\u1ec3n \u0111\u1ed9ng \u0111\u1ec1u. m\u1ed9t ch\u1ea5t \u0111i\u1ec3m B kh\u00e1c xu\u1ea5t ph\u00e1t t\u1eeb c\u00f9ng v\u1ecb tr\u00ed v\u1edbi A nh\u01b0ng ch\u1eadm h\u01a1n n\u00f3 12 gi\u00e2y v\u1edbi v\u1eadn t\u1ed1c nhanh d\u1ea7n \u0111\u1ec1u v\u00e0 \u0111u\u1ed5i k\u1ecbp A sau 8 gi\u00e2y (k\u1ec3 t\u1eeb l\u00fac B xu\u1ea5t ph\u00e1t). T\u00ecm v\u1eadn t\u1ed1c c\u1ee7a B t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

T\u1eeb c\u00f4ng th\u1ee9c v_{1<\/sub>=v0<\/sub>+at ta c\u00f3:<\/p>\n}

Gia t\u1ed1c tr\u1ecdng trong 8 gi\u00e2y \u0111\u1ea7u c\u1ee7a ch\u1ea5t \u0111i\u1ec3m A l\u00e0:<\/p>\n

<\/p>\n

Trong 8 gi\u00e2y \u0111\u1ea7u n\u00e0y, ch\u1ea5t \u0111i\u1ec3m A chuy\u1ec3n \u0111\u1ed9ng nhanh d\u1ea7n v\u1edbi v\u1eadn t\u1ed1c v(t)=3t\/4 , v\u1eady n\u00f3 \u0111\u1ecb \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0<\/p>\n

<\/p>\n

Sau 12 gi\u00e2y ti\u1ebfp theo ( khi m\u00e0 b\u1ecb B \u0111u\u1ed5i k\u1ecbp A), A \u0111i \u0111\u01b0\u1ee3c th\u1ec3m 6.12 = 72 m\u00e9t.<\/p>\n

Nh\u01b0 v\u1eady, khi b\u1ecb B \u0111u\u1ed5i k\u1ecbp, A v\u00e0 B \u0111i \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 24 + 72 = 96 m\u00e9t<\/p>\n

T\u1eeb c\u00f4ng th\u1ee9c<\/p>\n

<\/p>\n

suy ra gia t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m B l\u00e0:<\/p>\n

<\/p>\n

V\u1eady khi \u0111u\u1ed5i k\u1ecbp A, v\u1eadn t\u1ed1c c\u1ee7a b l\u00e0:<\/p>\n

v_{1<\/sub>=v0<\/sub>+at=0+3.8=24 (m\/s)<\/p>\n}

B\u00e0i 50 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ednh c\u00e1c t\u00ednh ph\u00e2n sau<\/p>\n

<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

<\/p>\n

B\u00e0i 51 (trang 176 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n

T\u00ednh di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi<\/p>\n

a) \u0110\u1ed3 th\u1ecb c\u00e1c h\u00e0m s\u1ed1 y=4-x^{2<\/sup>;y=-x+2<\/p>\n}

b) C\u00e1c \u0111\u01b0\u1eddng cong c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh x=4-4y^{2<\/sup>\u00a0v\u00e0 x=1-y4<\/sup><\/p>\n}

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

<\/p>\n

V\u1eady di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng c\u1ea7n t\u00ecm l\u00e0:<\/p>\n

<\/p>\n

b) Tung \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng cong l\u00e0 nghi\u1ec7m c\u1ee7a Ph\u01b0\u01a1ng tr\u00ecnh<\/p>\n

4-4y^{2<\/sup>=1-y4<\/sup>\u00a0<=> y4<\/sup>-4y4<\/sup>+3=0<\/p>\n}

<\/p>\n

X\u00e9t d\u1ea5u (y2<\/sup>-1)(y2<\/sup>-3) ta c\u00f3<\/p>\n\n\n\n\n\n\n

y<\/td>\n	-\u221e<\/td>\n	<\/td>\n	-\u221a3<\/td>\n	<\/td>\n	-1<\/td>\n	<\/td>\n	1<\/td>\n	<\/td>\n	\u221a3<\/td>\n	<\/td>\n	+\u221e<\/td>\n<\/tr>\n
y2<\/sup>\u00a0– 1<\/td>\n	<\/td>\n	+<\/td>\n	|<\/td>\n	+<\/td>\n	0<\/td>\n	–<\/td>\n	0<\/td>\n	+<\/td>\n	|<\/td>\n	+<\/td>\n	<\/td>\n<\/tr>\n
y2<\/sup>\u00a0– 3<\/td>\n	<\/td>\n	+<\/td>\n	0<\/td>\n	–<\/td>\n	|<\/td>\n	–<\/td>\n	|<\/td>\n	–<\/td>\n	0<\/td>\n	+<\/td>\n	<\/td>\n<\/tr>\n
(y2<\/sup>\u00a0– 1)(y2<\/sup>\u00a0– 3)<\/td>\n	<\/td>\n	+<\/td>\n	0<\/td>\n	–<\/td>\n	0<\/td>\n	+<\/td>\n	0<\/td>\n	–<\/td>\n	0<\/td>\n	+<\/td>\n	<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Di\u1ec7n t\u00edch h\u00ecnh ph\u1eb3ng c\u1ea7n t\u00ecm l\u00e0:<\/p>\n <\/p>\n Ch\u00fa \u00fd. Ta c\u00f3 th\u1ec3 l\u00e0m theo c\u00e1ch kh\u00e1c nh\u01b0 sau m\u00e0 kh\u00f4ng c\u1ea7n l\u1eadp b\u1ea3ng x\u00e9t d\u1ea5u:<\/p>\n V\u00ec hai \u0111\u01b0\u1eddng \u0111\u00e3 cho c\u1eaft nhau t\u1ea1i 4 \u0111i\u1ec3m c\u00f3 tung \u0111\u1ed9 l\u1ea7n l\u01b0\u1ee3t l\u00e0 -\u221a3; -1;1;\u221a3 n\u00ean m\u1ed7i kho\u1ea3ng (-\u221a3; -1);(-1;1);(1;\u221a3) th\u00ec bi\u1ec3u th\u1ee9c y4<\/sup>-4y2<\/sub>+3 gi\u1eef nguy\u00ean m\u1ed9t d\u1ea5u v\u1eady<\/p>\n <\/p>\n Ta c\u0169ng c\u00f3 th\u1ec3 d\u1ef1a v\u00e0o t\u00ednh \u0111\u1ed1i x\u1ee9ng qua Ox c\u1ee7a c\u1ea3 hai \u0111\u01b0\u1eddng cong \u0111\u1ec3 t\u00ednh g\u1ecdn h\u01a1n<\/p>\n <\/p>\n  <\/p>\n B\u00e0i 52 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n T\u00ednh di\u1ec7n t\u00edch c\u1ee7a c\u00e1c h\u00ecnh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi<\/p>\n a) Parabol y=x2<\/sup>-2x+2, ti\u1ebfp tuy\u1ebfn n\u00f3 t\u1ea1i \u0111i\u1ec3m M(3; 5) v\u00e0 tr\u1ee5c tung.<\/p>\n b) Parabol y=-x2<\/sup>+4x-3 v\u00e0 c\u00e1c ti\u1ebfp tuy\u1ebfn c\u1ee7a n\u00f3 t\u1ea1i c\u00e1c \u0111i\u1ec3m A(0; -3) v\u00e0 B(3; 0)<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n a) y=x2<\/sup>-2x+2<\/p>\n y’=2x-2;y’ (3)=4<\/p>\n => Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn t\u1ea1i M l\u00e0:<\/p>\n y-5=4(x-3) hay y=4x-7<\/p>\n Di\u1ec7n t\u00edch c\u1ea7n t\u00ecm l\u00e0:<\/p>\n <\/p>\n b) y=-x2<\/sup>+4x-3<\/p>\n y’=-2x+4<\/p>\n y’ (3)=-2<\/p>\n Ti\u1ebfp tuy\u1ebfn t\u1ea1i A l\u00e0: y=4x-3<\/p>\n Ti\u1ebfp tuy\u1ebfn t\u1ea1i B l\u00e0: y=-2x+6<\/p>\n Hai ti\u1ebfp tuy\u1ebfn n\u00e0y c\u1eaft nhau t\u1ea1i \u0111i\u1ec3m c\u00f3 ho\u00e0nh \u0111\u1ed9 l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n 4x-3=-2x+6 <=> x=3\/2<\/p>\n D\u1ef1a v\u00e0o h\u00ecnh v\u1ebd ta c\u00f3 di\u1ec7n t\u00edch c\u1ea7n t\u00ecm l\u00e0:<\/p>\n <\/p>\n  <\/p>\n B\u00e0i 53 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n T\u00ednh th\u1ec3 t\u00edch c\u1ee7a v\u1eadt th\u1ec3 n\u1eb1m gi\u1eefa hai m\u1eb7t ph\u1eb3ng x = 0 v\u00e0 x = 2 bi\u1ebft r\u1eb1ng thi\u1ebft di\u1ec7n c\u1ee7a v\u1eadt th\u1ec3 b\u1ecb c\u1eaft b\u1edfi m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c Ox t\u1ea1i \u0111i\u1ec3m c\u00f3 ho\u00e0nh \u0111\u1ed9 x (0 \u2264 x \u2264 2) l\u00e0 m\u1ed9t n\u1eeda h\u00ecnh tr\u00f2n \u0111\u01b0\u1eddng k\u00ednh \u221a5 x2<\/sup><\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n Thi\u1ebft di\u1ec7n c\u1ee7a v\u1eadt th\u1ec3 c\u00f3 di\u1ec7n t\u00edch l\u00e0:<\/p>\n <\/p>\n V\u1eady th\u1ec3 t\u00edch c\u1ea7n t\u00ecm l\u00e0:<\/p>\n <\/p>\n B\u00e0i 54 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n X\u00e9t h\u00ecnh gi\u1edbi h\u1ea1n \u0111\u01b0\u1eddng hyperbol y=2\/x v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng y = 1; y =4; x = 0. T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u00f2n xoay t\u1ea1o th\u00e0nh khi quay h\u00ecnh \u0111\u00f3 quanh tr\u1ee5c tung.<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n <\/p>\n B\u00e0i 55 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n Cho h\u00ecnh ph\u1eb3ng A \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/p>\n <\/p>\n v\u00e0 hai tr\u1ee5c t\u1ecda \u0111\u1ed9. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o th\u00e0nh khi quay A quanh tr\u1ee5c ho\u00e0nh.<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n <\/p>\n B\u00e0i 56 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n Cho h\u00ecnh ph\u1eb3ng A \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi \u0111\u01b0\u1eddng cong c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh x(y + 1) =2 v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng x = 0; y =0; y = 3. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o \u0111\u01b0\u1ee3c khi A quay quanh tr\u1ee5c tung.<\/p>\n a) Quanh tr\u1ee5c ho\u00e0nh.<\/p>\n b) Quanh tr\u1ee5c tung<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n <\/p>\n a) \u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 y=\u221ax c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng y = 2 t\u1ea1i \u0111i\u1ec3m c\u00f3 ho\u00e0nh \u0111\u1ed9 l\u00e0 4.<\/p>\n Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o \u0111\u01b0\u1ee3c b\u1eb1ng th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o th\u00e0nh khi quay mi\u1ec1n h\u00ecnh ch\u1eef nh\u1eadt OMNP quanh Ox tr\u1eeb \u0111i th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o th\u00e0nh khi quay mi\u1ec1n tam gi\u00e1c cong ONP quanh Ox.<\/p>\n <\/p>\n b) Th\u1ec3 t\u00edch c\u1ea7n t\u00ecm l\u00e0:<\/p>\n <\/p>\n B\u00e0i 57 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n Cho h\u00ecnh ph\u1eb3ng A gi\u1edbi h\u1ea1n b\u1edfi \u0111\u01b0\u1eddng cong y=x1\/2<\/sup>\u00a0ex\/2<\/sup>\u00a0v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng x = 1; x = 2, y =0. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o th\u00e0nh khi quay a quang tr\u1ee5c ho\u00e0nh.<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n <\/p>\n B\u00e0i 58 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n Cho h\u00ecnh ph\u1eb3ng A gi\u1edbi h\u1ea1n b\u1edfi \u0111\u01b0\u1eddng cong<\/p>\n v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng x = 1; x = 2, y =0. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay t\u1ea1o th\u00e0nh khi quay a quang tr\u1ee5c ho\u00e0nh.<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n <\/p>\n B\u00e0i 59 (trang 177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/p>\n Cho h\u00ecnh ph\u1eb3ng A \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi \u0111\u01b0\u1eddng cong c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh y2<\/sup>=x3<\/sup>\u00a0v\u00e0 c\u00e1c Ph\u01b0\u01a1ng tr\u00ecnh y = 0; x = 1. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c khi quay A.<\/p>\n a) Quanh tr\u1ee5c ho\u00e0nh<\/p>\n b) Quanh tr\u1ee5c tung<\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n y2<\/sup>=x3<\/sup>\u00a0<=> y=\u00b1\u221a(x3<\/sup>\u00a0) <=> x=\u221b(y2<\/sup>\u00a0)<\/p>\n <\/p>\n a) Ta th\u1ea5y \u0111\u01b0\u1eddng cong y^2=x^3 c\u00f3 2 nh\u00e1nh \u0111\u1ed1i x\u1ee9ng qua Ox. V\u1eady khi quay quanh tr\u1ee5c ho\u00e0nh ta c\u00f3 v\u1eadt th\u1ec3 xoay tr\u00f2n c\u00f3 th\u1ec3 t\u00edch:<\/p>\n <\/p>\n \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":" B\u00e0i t\u1eadp (trang 175-176-177 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao) B\u00e0i 41 (trang 175 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao): T\u00ecm nguy\u00ean h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 sau: L\u1eddi gi\u1ea3i: Ch\u00fa \u00fd: ta c\u00f3 th\u1ec3 t\u00ecm nguy\u00ean h\u00e0m n\u00e0y theo c\u00e1ch kh\u00f4ng \u0111\u01b0a ra bi\u1ebfn u nh\u01b0 sau: B\u00e0i 42 (trang 175 sgk Gi\u1ea3i T\u00edch […]<\/p>\n","protected":false},"author":3,"featured_media":23020,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\n