{"common":{"save":0,"post_id":"7610","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5899","post_id":"7610","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho <span class=\"math-tex\">$\\displaystyle\\int\\limits_{-1}^{2}f(x)dx=2$<\/span> và <span class=\"math-tex\">$\\displaystyle\\int\\limits_{-1}^{2}g(x)dx=-1$<\/span>. Khi \u0111ó <span class=\"math-tex\">$\\displaystyle\\int\\limits_{-1}^{2}[x+2f(x)+3g(x)]dx$<\/span> b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{5}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{7}{2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{17}{2}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{11}{2}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{5}{2}$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$\\displaystyle\\int\\limits_{-1}^{2}[x+2f(x)+3g(x)]dx$<\/span> <\/p><p>= <span class=\"math-tex\">$\\displaystyle\\int\\limits_{-1}^{2}xdx+2\\displaystyle\\int\\limits_{-1}^{2}f(x)dx+3\\displaystyle\\int\\limits_{-1}^{2}g(x)dx$<\/span><\/p><p>= <span class=\"math-tex\">$\\dfrac{x^2}{2}\\bigg|^2_{-1}$<\/span> + 2.2 + 3.(–1)<\/p><p>= <span class=\"math-tex\">$\\dfrac{3}{2}+4-3$<\/span><\/p><p>= <span class=\"math-tex\">$\\dfrac{5}{2}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-19 08:58:49","option_type":"math","len":0},{"id":"5900","post_id":"7610","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho <span class=\"math-tex\">$\\displaystyle\\int\\limits_{0}^{5}f(x)dx=-2$<\/span>. Tích phân <span class=\"math-tex\">$\\displaystyle\\int\\limits_{0}^{5}[4f(x)-3x^2]dx$<\/span> b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> –143","<strong>B.<\/strong> –130","<strong>C.<\/strong> –120","<strong>D.<\/strong> –133"],"correct":"4","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> –133.<\/span><\/p><p><span class=\"math-tex\">$\\displaystyle\\int\\limits_{0}^{5}[4f(x)-3x^2]dx$<\/span> <\/p><p>= <span class=\"math-tex\">$4\\displaystyle\\int\\limits_{0}^{5}f(x)dx-\\displaystyle\\int\\limits_{0}^{5}3x^2dx$<\/span><\/p><p>= 4.(–2) – <span class=\"math-tex\">$x^3\\;\\bigg|^5_0$<\/span><\/p><p>= –8 – 125<\/p><p>= –133.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-19 09:07:17","option_type":"txt","len":1},{"id":"5901","post_id":"7610","mon_id":"1159285","chapter_id":"1159380","question":"<p>Tính tích phân <span class=\"math-tex\">$I=\\displaystyle\\int\\limits_{0}^{2}(2x+1)dx$<\/span>.<\/p>","options":["<strong>A.<\/strong> 5","<strong>B.<\/strong> 6","<strong>C.<\/strong> 2","<strong>D.<\/strong> 4"],"correct":"2","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 6.<\/span><\/p><p><span class=\"math-tex\">$I=\\displaystyle\\int\\limits_{0}^{2}(2x+1)dx$<\/span><\/p><p> <span class=\"math-tex\">$=(x^2+x)\\;\\bigg|_0^2$<\/span><\/p><p> <span class=\"math-tex\">$=2^2+2-0^2-0$<\/span><\/p><p> <span class=\"math-tex\">$=6$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-11-19 09:11:01","option_type":"txt","len":0}]}
