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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài tập cuối chương 4 - NGUYÊN HÀM VÀ TÍCH PHÂNBài tập cơ bản
{"common":{"save":0,"post_id":"8204","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5993","post_id":"8204","mon_id":"1159285","chapter_id":"1159380","question":"<p>H\u1ecd t\u1ea5t c\u1ea3 các nguyên hàm c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=\\sin x-2x+1$<\/span> là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\cos x-x^2+x$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$-\\cos x-x^2+x+C$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\cos x-x^2+x+C$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$-\\cos x-\\dfrac{x^2}{2}+x+C$<\/span>"],"correct":"2","level":"1","hint":"<p>S\u1eed d\u1ee5ng công th\u1ee9c nguyên hàm <\/p><p><span class=\"math-tex\">$\\int kf(x)dx=k\\int f(x)dx$<\/span> v\u1edbi k là h\u1eb1ng s\u1ed1 khác 0.<\/p><p><span class=\"math-tex\">$\\int [f(x)+g(x)]dx=\\int f(x)dx+\\int g(x)dx$<\/span><\/p><p><span class=\"math-tex\">$\\int [f(x)-g(x)]dx=\\int f(x)dx-\\int g(x)dx$<\/span><\/p><p><span class=\"math-tex\">$\\int \\sin xdx=-\\cos x + C$<\/span><\/p><p><span class=\"math-tex\">$\\int x^\\alpha dx=\\dfrac{x^{\\alpha+1}}{\\alpha+1} + C\\;(\\alpha\\ne-1)$<\/span><\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#1abc9c;\"><strong>B.<\/strong> <span class=\"math-tex\">$-\\cos x-x^2+x+C$<\/span><\/span><\/p><p><span class=\"math-tex\">$f(x)=\\sin x-2x+1$<\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\int f(x)dx=\\int (\\sin x-2x+1)dx=\\int \\sin xdx-2\\int xdx+\\int dx=-\\cos x-x^2+x+C$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-22 11:16:18","option_type":"math","len":0},{"id":"5995","post_id":"8204","mon_id":"1159285","chapter_id":"1159380","question":"<p>H\u1ecd t\u1ea5t c\u1ea3 các nguyên hàm c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=e^x+1$<\/span> là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$e^x+C$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$e^x+x$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$e^x+x+C$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$-e^x+x+C$<\/span>"],"correct":"3","level":"1","hint":"<p>S\u1eed d\u1ee5ng công th\u1ee9c tính nguyên hàm<\/p><p><span class=\"math-tex\">$\\int [f(x)+g(x)]dx=\\int f(x)dx+\\int g(x)dx$<\/span><\/p><p><span class=\"math-tex\">$\\int e^xdx=e^x+C$<\/span><\/p><p><span class=\"math-tex\">$\\int dx=x+C$<\/span><\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$e^x+x+C$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\int (e^x+1)dx=\\int e^xdx+\\int dx=e^x+x+C$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-22 11:18:34","option_type":"math","len":0},{"id":"5996","post_id":"8204","mon_id":"1159285","chapter_id":"1159380","question":"<p>H\u1ecd t\u1ea5t c\u1ea3 các nguyên hàm c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=\\dfrac{3x^3-2x^2+5}{x}$<\/span> là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x^3-x^2+5\\ln x+C$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x^3-x^2-5\\ln x+C$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x^3-x^2+5\\ln|x|$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x^3-x^2+5\\ln|x|+C$<\/span>"],"correct":"4","level":"1","hint":"<p>S\u1eed d\u1ee5ng công th\u1ee9c nguyên hàm <\/p><p><span class=\"math-tex\">$\\int [f(x)+g(x)]dx=\\int f(x)dx+\\int g(x)dx$<\/span><\/p><p><span class=\"math-tex\">$\\int x^\\alpha dx=\\dfrac{x^{\\alpha+1}}{\\alpha+1} + C\\;(\\alpha\\ne-1)$<\/span><\/p><p><span class=\"math-tex\">$\\int \\dfrac{dx}{x}=\\ln|x|+C\\;(x\\ne0)$<\/span><\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$x^3-x^2+5\\ln|x|+C$<\/span><\/span><\/p><p>Ta có:<\/p><p><span class=\"math-tex\">$\\int\\dfrac{3x^3-2x^2+5}{x}dx=\\int\\bigg(3x^2-2x+\\dfrac{5}{x}\\bigg)dx$<\/span><\/p><p><span class=\"math-tex\">$=3\\int x^2dx-2\\int xdx+5\\int\\dfrac{1}{x}dx$<\/span> <span class=\"math-tex\">$=x^3-x^2+5\\ln|x|+C$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-22 11:22:25","option_type":"math","len":0}]}