Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"7608","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5844","post_id":"7608","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho F(x) là m\u1ed9t nguyên hàm c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=e^x+2x$<\/span> tho\u1ea3 mãn <span class=\"math-tex\">$F(0)=\\dfrac{3}{2}$<\/span>. Tìm F(x).<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$e^x+x^2+\\dfrac{1}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$e^x+x^2+\\dfrac{5}{2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$e^x+x^2+\\dfrac{3}{2}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$2e^x+x^2-\\dfrac{1}{2}$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$e^x+x^2+\\dfrac{1}{2}$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$F(x)=\\int (e^x+2x)dx=e^x+x^2+C$<\/span> .<\/p><p>Vì <span class=\"math-tex\">$F(0)=\\dfrac{3}{2}$<\/span> nên <span class=\"math-tex\">$e^0+0^2+C=\\dfrac{3}{2}$<\/span>, suy ra C = <span class=\"math-tex\">$\\dfrac{1}{2}$<\/span>.<\/p><p>V\u1eady <span style=\"color:#16a085;\"><span class=\"math-tex\">$F(x)=e^x+x^2+\\dfrac{1}{2}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-10-18 02:59:44","option_type":"math","len":0},{"id":"5846","post_id":"7608","mon_id":"1159285","chapter_id":"1159380","question":"<p>Cho F(x) = <span class=\"math-tex\">$\\displaystyle\\int\\sin\\dfrac{x}{2}dx$<\/span>. Bi\u1ebft <span class=\"math-tex\">$F(\\pi)=1$<\/span>. M\u1ec7nh \u0111\u1ec1 nào \u0111úng?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$F(0)\\in(2;3)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$F(0)\\in(-4;-2)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$F(0)\\in(0;1)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$F(0)\\in(-2;0)$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$F(0)\\in(-2;0)$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$F(x)=\\displaystyle\\int\\sin\\dfrac{x}{2}dx=-2\\cos\\dfrac{x}{2}+C$<\/span> .<\/p><p>Mà <span class=\"math-tex\">$F(\\pi)=1$<\/span> nên <span class=\"math-tex\">$-2\\cos\\dfrac{\\pi}{2}+C=1$<\/span>, suy ra C = 1.<\/p><p>Nên <span class=\"math-tex\">$F(x)=-2\\cos\\dfrac{x}{2}+1$<\/span>.<\/p><p>Khi \u0111ó <span class=\"math-tex\">$F(0)=-2\\cos0+1=-1\\in(-2;0)$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-10-18 03:03:56","option_type":"math","len":0},{"id":"5858","post_id":"7608","mon_id":"1159285","chapter_id":"1159380","question":"<p>Tìm nguyên hàm F(x) c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=\\sin x+\\cos x$<\/span> tho\u1ea3 mãn <span class=\"math-tex\">$F\\bigg(\\dfrac{\\pi}{2}\\bigg)=2$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$F(x)=-\\cos x+\\sin x+3$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$F(x)=-\\cos x+\\sin x-1$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$F(x)=-\\cos x+\\sin x+1$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$F(x)=\\cos x-\\sin x+3$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$F(x)=-\\cos x+\\sin x+1$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$F(x)=\\int f(x)dx=\\int(\\sin x+\\cos x)dx=-\\cos x+\\sin x+C$<\/span>.<\/p><p>Mà <span class=\"math-tex\">$F\\bigg(\\dfrac{\\pi}{2}\\bigg)=2$<\/span> nên <span class=\"math-tex\">$-\\cos \\dfrac{\\pi}{2}+\\sin \\dfrac{\\pi}{2}+C=2$<\/span>, suy ra C = 1.<\/p><p>V\u1eady <span style=\"color:#16a085;\"><span class=\"math-tex\">$F(x)=-\\cos x+\\sin x+1$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-10-19 01:44:50","option_type":"math","len":0}]}