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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài tập cuối chương 4 - NGUYÊN HÀM VÀ TÍCH PHÂNBài tập nâng cao
{"common":{"save":0,"post_id":"8207","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5992","post_id":"8207","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho hình ph\u1eb3ng gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb hàm s\u1ed1 <span class=\"math-tex\">$y=\\sin x$<\/span> , tr\u1ee5c Ox và các \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$x=0$<\/span>, <span class=\"math-tex\">$x=\\pi$<\/span> quay quanh tr\u1ee5c Ox. Công th\u1ee9c tính th\u1ec3 tích kh\u1ed1i tròn xoay t\u1ea1o thành là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\displaystyle\\int\\limits_{0}^{\\pi}\\sin xdx$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}\\sin xdx$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-22 11:11:39","option_type":"math","len":0},{"id":"5994","post_id":"8207","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho hình ph\u1eb3ng (D) \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi các \u0111\u01b0\u1eddng <span class=\"math-tex\">$x=0$<\/span>, <span class=\"math-tex\">$x=\\pi$<\/span>, <span class=\"math-tex\">$y=0$<\/span> và <span class=\"math-tex\">$y=-\\sin x$<\/span>. Th\u1ec3 tích V c\u1ee7a kh\u1ed1i tròn xoay t\u1ea1o thành khi quay (D) xung quanh tr\u1ee5c Ox \u0111\u01b0\u1ee3c tính theo công th\u1ee9c<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}|\\sin x|dx$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\pi\\bigg|\\displaystyle\\int\\limits_{0}^{\\pi}(-\\sin x)dx\\bigg|$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>.<\/span><\/p><p>V = <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}(-\\sin x)^2dx$<\/span> = <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\pi}\\sin^2xdx$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-22 11:16:53","option_type":"math","len":0},{"id":"5997","post_id":"8207","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho hình ph\u1eb3ng (H) gi\u1edbi h\u1ea1n b\u1edfi \u0111\u1ed3 th\u1ecb hàm s\u1ed1 <span class=\"math-tex\">$y=e^x$<\/span>, các \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$x=0$<\/span>, <span class=\"math-tex\">$x=\\ln3$<\/span> và tr\u1ee5c hoành. Th\u1ec3 tích kh\u1ed1i tròn xoay sinh b\u1edfi (H) khi quay quanh tr\u1ee5c hoành là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$2\\pi$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$4\\pi$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$4$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\pi$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$4\\pi$<\/span>.<\/span><\/p><p>V = <span class=\"math-tex\">$\\pi\\displaystyle\\int\\limits_{0}^{\\ln3}e^{2x}dx=\\pi.\\dfrac{1}{2}e^{2x}\\bigg|_0^{\\ln3}=4\\pi$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-22 11:23:50","option_type":"math","len":0}]}