{"common":{"save":0,"post_id":"8086","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5942","post_id":"8086","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho hai h&agrave;m s\u1ed1 <span class=\"math-tex\">$f(x)$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$g(x)$<\/span>&nbsp;li&ecirc;n t\u1ee5c tr&ecirc;n&nbsp;<span class=\"math-tex\">$[a;b]$<\/span>.&nbsp;Di\u1ec7n t&iacute;ch h&igrave;nh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb c\u1ee7a c&aacute;c h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$y=f(x)$<\/span>, <span class=\"math-tex\">$y=g(x)$<\/span> v&agrave; c&aacute;c \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$x = a$<\/span>, <span class=\"math-tex\">$x = b$<\/span> b\u1eb1ng&nbsp;<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\bigg|\\int\\limits_a^b\\Big[f(x)-g(x)\\Big]dx\\bigg|$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\bigg|\\int\\limits_a^b\\Big[f(x)+g(x)\\Big]dx\\bigg|$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\int\\limits_a^b\\Big|f(x)-g(x)\\Big|dx$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\int\\limits_a^b\\Big[f(x)-g(x)\\Big]dx$<\/span>"],"correct":"3","level":"1","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$\\int\\limits_a^b\\Big|f(x)-g(x)\\Big|dx$<\/span><\/span><\/p><p>Theo l&yacute; thuy\u1ebft th&igrave; di\u1ec7n t&iacute;ch h&igrave;nh ph\u1eb3ng \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi&nbsp;\u0111\u1ed3 th\u1ecb c\u1ee7a c&aacute;c \u0111\u01b0\u1eddng&nbsp;<span class=\"math-tex\">$y=f(x)$<\/span>, <span class=\"math-tex\">$y=g(x)$<\/span>,&nbsp;<span class=\"math-tex\">$x = a$<\/span>, <span class=\"math-tex\">$x = b\\;$<\/span>\u0111\u01b0\u1ee3c t&iacute;nh theo c&ocirc;ng th\u1ee9c&nbsp;<span class=\"math-tex\">$S=\\int\\limits_a^b\\Big|f(x)-g(x)\\Big|dx$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-28 07:58:40","option_type":"math","len":0},{"id":"5943","post_id":"8086","mon_id":"1159285","chapter_id":"1159380","question":"<p>G\u1ecdi S l&agrave; di\u1ec7n t&iacute;ch c\u1ee7a h&igrave;nh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi c&aacute;c&nbsp;\u0111\u01b0\u1eddng&nbsp;<span class=\"math-tex\">$y=3^x,y=0,x=0,x=2$<\/span>. M\u1ec7nh \u0111\u1ec1 n&agrave;o d\u01b0\u1edbi \u0111&acirc;y <strong>\u0111&uacute;ng<\/strong>?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$S=\\int\\limits_a^b3^xdx$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$S=\\pi\\int\\limits_a^b3^xdx$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$S=\\int\\limits_a^b3^{2x}dx$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$S=\\pi\\int\\limits_a^b3^{2x}dx$<\/span>"],"correct":"1","level":"1","hint":"<p>Theo l&yacute; thuy\u1ebft th&igrave; di\u1ec7n t&iacute;ch h&igrave;nh ph\u1eb3ng \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi&nbsp;\u0111\u1ed3 th\u1ecb c\u1ee7a c&aacute;c \u0111\u01b0\u1eddng&nbsp;<span class=\"math-tex\">$y=f(x)$<\/span>, <span class=\"math-tex\">$y=g(x)$<\/span>,&nbsp;<span class=\"math-tex\">$x = a$<\/span>, <span class=\"math-tex\">$x = b\\;$<\/span>\u0111\u01b0\u1ee3c t&iacute;nh theo c&ocirc;ng th\u1ee9c&nbsp;<span class=\"math-tex\">$S=\\int\\limits_a^b\\Big|f(x)-g(x)\\Big|dx$<\/span>.<\/p>","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$S=\\int\\limits_a^b3^xdx$<\/span><\/span><\/p><p>Di\u1ec7n t&iacute;ch h&igrave;nh ph\u1eb3ng \u0111&atilde; cho \u0111\u01b0\u1ee3c t&iacute;nh b\u1edfi c&ocirc;ng th\u1ee9c&nbsp;<span class=\"math-tex\">$S=\\int\\limits_a^b3^xdx$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-28 07:59:59","option_type":"math","len":0},{"id":"5944","post_id":"8086","mon_id":"1159285","chapter_id":"1159380","question":"<p>Di\u1ec7n t&iacute;ch h&igrave;nh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$y=(x-2)^2-1$<\/span>, tr\u1ee5c ho&agrave;nh v&agrave; hai \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$x = 1,x=2$<\/span>&nbsp;b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{3}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{7}{3}$<\/span>"],"correct":"1","level":"1","hint":"<p>Di\u1ec7n t&iacute;ch h&igrave;nh ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$y=f(x)$<\/span>, tr\u1ee5c ho&agrave;nh Ox (y = 0)&nbsp;v&agrave; hai \u0111\u01b0\u1eddng th\u1eb3ng x =a v&agrave; x = b \u0111\u01b0\u1ee3c t&iacute;nh b\u1edfi c&ocirc;ng th\u1ee9c:&nbsp;<span class=\"math-tex\">$S=\\int\\limits_a^b|f(x)|dx$<\/span>.<\/p>","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{2}{3}$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$S=\\int\\limits_1^2|(x-2)^2-1|dx$<\/span>&nbsp;<span class=\"math-tex\">$=\\int\\limits_1^2|x^2-4x+3|dx$<\/span>&nbsp;<span class=\"math-tex\">$=\\bigg|\\int\\limits_1^2(x^2-4x+3)dx\\bigg|=\\dfrac{2}{3}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-28 08:08:00","option_type":"math","len":0}]}