{"id":6735,"date":"2021-07-21T00:09:33","date_gmt":"2021-07-20T15:09:33","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6735"},"modified":"2022-03-06T19:47:56","modified_gmt":"2022-03-06T10:47:56","slug":"fundamental-theorem-of-calculus","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/fundamental-theorem-of-calculus\/","title":{"rendered":"\ubbf8\uc801\ubd84\uc758 \uae30\ubcf8\uc815\ub9ac"},"content":{"rendered":"<div style=\"display: none; visibility: hidden;\">\n<style type=\"text\/css\">\n\timg.mfp-img { background-color: white; }\n<\/style>\n<p><!--\n\\[\n\\newcommand{\\vecf}{{\\mathbf{f}}}\n\\newcommand{\\vecL}{{\\mathbf{L}}}\n\\newcommand{\\vecR}{{\\mathbb{R}}}\n\\newcommand{\\imI}{\\boldsymbol{i}}\n\\]\n-->\n<\/div>\n<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 6\uc7a5 2\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p>7\uc7a5 1\uc808\uc5d0\uc11c \uc815\uc801\ubd84\uc744 \uc815\uc758\ud558\uace0 \uc5b4\ub5a0\ud55c \ud568\uc218\uac00 \uc801\ubd84 \uac00\ub2a5\ud55c\uc9c0 \uc0b4\ud3b4\ubcf4\uc558\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \uc815\uc801\ubd84\uc744 \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<p>\\(a < b\\)\uc774\uace0 \\(f\\)\uac00 \\(I=[a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec\n\\[G(x) = \\int_a^x f(t) dt\\]\n\ub77c\uace0 \ud558\uc790. \uc774\uc81c \\(a\\le x < b\\)\ub77c\uace0 \ud558\uace0 \\(\\Delta x\\)\uac00 \\(a < x + \\Delta x \\le b\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc791\uc740 \uc591\uc218\ub77c\uace0 \ud558\uc790. \ub2eb\ud78c\uad6c\uac04 \\(\\left[ x ,\\, x+\\Delta x \\right]\\)\uc5d0\uc11c \\(f\\)\uc758 \ucd5c\uc19f\uac12\uacfc \ucd5c\ub313\uac12\uc744 \uac01\uac01 \\(m,\\) \\(M\\)\uc774\ub77c\uace0 \ud558\uc790. (\uc5ec\uae30\uc11c \\(m\\)\uacfc \\(M\\)\uc740 \\(\\Delta x\\)\uc5d0 \ub530\ub77c \ubcc0\ud558\ub294 \uac12\uc784\uc744 \uc0dd\uac01\ud558\uc790.) \ub2e4\uc74c \uadf8\ub9bc\uc744 \ubcf4\uc790.<\/p>\n<div class=\"margintop1 marginbottom1\">\n<a href=\"\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1.png\" data-rel=\"penci-gallery-image-content\" ><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1.png\" alt=\"\" width=\"318\" height=\"213\" class=\"aligncenter size-full wp-image-7814\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1.png 1592w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-300x201.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-1024x686.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-768x514.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-1536x1029.png 1536w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-1170x783.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-585x392.png 585w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_702_1-263x175.png 263w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/a>\n<\/div>\n<p>\ubc11\ubcc0\uc758 \uae38\uc774\uac00 \\(\\Delta x\\)\uc774\uace0 \ub192\uc774\uac00 \\(m\\)\uc778 \uc9c1\uc0ac\uac01\ud615, \ubc11\ubcc0\uc758 \uae38\uc774\uac00 \\(\\Delta x\\)\uc774\uace0 \ub192\uc774\uac00 \\(M\\)\uc778 \uc9c1\uc0ac\uac01\ud615\uc758 \ub113\uc774\ub97c \uace0\ub824\ud558\uba74 \ub2e4\uc74c \ubd80\ub4f1\uc2dd\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[m\\Delta x \\le G(x+\\Delta x) &#8211; G(x) \\le M\\Delta x\\]<br \/>\n\uac01 \uc2dd\uc744 \\(\\Delta x\\)\ub85c \ub098\ub204\uba74 \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.<br \/>\n\\[m \\le \\frac{G(x+\\Delta x) &#8211; G(x)}{\\Delta x} \\le M.\\]<br \/>\n\ud568\uc218 \\(f\\)\uac00 \\(\\left[ x,\\, x+\\Delta x\\right]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ubbc0\ub85c<br \/>\n\\[f( \\xi_1 ) = m ,\\quad f(\\xi _2 ) = M\\]<br \/>\n\uc778 \\(\\xi_1 \\)\uacfc \\(\\xi _2\\)\uac00 \\(\\left[ x,\\, x+\\Delta x \\right]\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uc989<br \/>\n\\[f(\\xi_1 ) \\le \\frac{G(x+\\Delta x) &#8211; G(x)}{\\Delta x} \\le f(\\xi_2 )\\]<br \/>\n\uc774\ub2e4. \\(\\Delta x \\rightarrow 0^+\\)\uc77c \ub54c \\(\\xi_1 \\rightarrow x\\)\uc774\uace0 \\(\\xi_2 \\rightarrow x\\)\uc774\uba70, \\(f\\)\uac00 \\(x\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ubbc0\ub85c<br \/>\n\\[f(\\xi_1 ) \\rightarrow f(x) ,\\quad f(\\xi_2 ) \\rightarrow f(x)\\]<br \/>\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(x\\)\uc5d0\uc11c \\(G\\)\uc758 \uc6b0\ubbf8\ubd84\uacc4\uc218\ub294<br \/>\n\\[G_r &#8216; (x) = f(x)\\]<br \/>\n\uc774\ub2e4. \\(a\\le x+\\Delta x < x \\le b\\)\uc77c \ub54c\ub3c4 \ub9c8\ucc2c\uac00\uc9c0 \ubc29\ubc95\uc73c\ub85c \\(x\\)\uc5d0\uc11c \\(G\\)\uc758 \uc88c\ubbf8\ubd84\uacc4\uc218\uac00\n\\[G_l ' (x) = f(x)\\]\n\uac00 \ub428\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.<\/p>\n<p>\uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 6.2.1. (\uc801\ubd84\uc73c\ub85c \uc815\uc758\ub41c \ud568\uc218)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\(I = [a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\uc774\uace0<br \/>\n\\[G(x) = \\int_a^x f(t) dt\\]<br \/>\n\ub77c\uace0 \ud558\uc790 \uadf8\ub7ec\uba74 \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec \\(G &#8216; (x) = f(x)\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\uc55e\uc758 \uac00\uc815\uc744 \uadf8\ub300\ub85c \ub454 \uc0c1\ud0dc\uc5d0\uc11c, \\(F\\)\uac00 \\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \ud55c \uc5ed\ub3c4\ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[F &#8216; (x) = f(x) = G &#8216; (x)\\]<br \/>\n\uc774\ubbc0\ub85c \uc0c1\uc218 \\(C\\)\uac00 \uc874\uc7ac\ud558\uc5ec \uc784\uc758\uc758 \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[G(x) = F(x) +C\\]<br \/>\n\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4. \uc774 \ub4f1\uc2dd\uc5d0\uc11c \\(x\\)\uc5d0 \\(a\\)\ub97c \ub300\uc785\ud558\uba74<br \/>\n\\[F(a) +C = G(a)=0\\]<br \/>\n\uc774\ubbc0\ub85c \\(C = -F(a)\\)\ub97c \uc5bb\ub294\ub2e4. \uc989<br \/>\n\\[G(x) = F(x) &#8211; F(a)\\]<br \/>\n\uc774\ub2e4. \uc774 \ub4f1\uc2dd\uc5d0\uc11c \\(x\\)\uc5d0 \\(b\\)\ub97c \ub300\uc785\ud558\uba74<br \/>\n\\[G(b) = F(b) &#8211; F(a)\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \\(G(b)\\)\ub97c \uc801\ubd84 \uae30\ud638\ub85c \ubc14\uafb8\uc5b4 \ub098\ud0c0\ub0b4\uba74<br \/>\n\\[\\int_a^b f(x)dx = F(b) -F(a)\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4.<\/p>\n<p>\uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 6.2.2. (\ubbf8\uc801\ubd84\uc758 \uae30\ubcf8\uc815\ub9ac)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\(I=[a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\uc774\uace0, \\(F\\)\uac00 \\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uc5ed\ub3c4\ud568\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74<br \/>\n\\[\\int_a^b f(x) dx = F(b) -F(a)\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\ubbf8\uc801\ubd84\uc758 \uae30\ubcf8\uc815\ub9ac\uc5d0\uc11c \ub4f1\uc2dd\uc758 \uc6b0\ubcc0\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud55c\ub2e4.<br \/>\n\\[\\int_a^b f(x) dx = F(x) \\bigg\\vert_a^b\\]<br \/>\n\ub610\ub294<br \/>\n\\[\\int_a^b f(x) dx = \\bigg[ F(x) \\bigg]_a^b  .\\]<br \/>\n\\(F(x)\\)\uac00 \ud558\ub098\uc758 \ud56d\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4\uba74 \ub450 \ud45c\ud604 \uc911 \uc5b4\ub290 \uac83\uc744 \uc0ac\uc6a9\ud574\ub3c4 \ubb34\ubc29\ud558\ub2e4. \\(F(x)\\)\uac00 \ub458 \uc774\uc0c1\uc758 \ud56d\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4\uba74 \ub450 \ubc88\uc9f8 \ud45c\ud604\uc744 \uc368\uc57c \ud558\uba70, \ub450 \ubc88\uc9f8 \ud45c\ud604\uc744 \uc4f0\uace0 \uc2f6\ub2e4\uba74 \\(F(x)\\)\uc758 \ud56d \uc804\uccb4\ub97c \uad04\ud638\ub85c \ubb36\uc73c\uba74 \ub41c\ub2e4.<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 6.2.1.<\/span> \ub2e4\uc74c \uc801\ubd84\uc744 \uad6c\ud558\uc2dc\uc624.<br \/>\n\\[\\int_0^1 x \\,dx .\\]\n<\/p>\n<p class=\"margintop1\"><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\\(f(x) =x ,\\) \\(F(x) = \\frac{1}{2} x^2\\)\uc774\ub77c\uace0 \ud558\uba74 \\(F &#8216; = f\\)\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ubbf8\uc801\ubd84\uc758 \uae30\ubcf8 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[\\int_0^1 x\\,dx = \\int_0^1 f(x) dx = F(1) &#8211; F(0) = \\frac{1}{2} -0 = \\frac{1}{2}\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 6.2.2.<\/span> \ub2e4\uc74c \uc801\ubd84\uc744 \uad6c\ud558\uc2dc\uc624.<br \/>\n\\[\\int_0^1 x^2 \\,dx .\\]\n<\/p>\n<p class=\"margintop1\"><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\\(g(x) =x^2 ,\\) \\(G(x) = \\frac{1}{3} x^2\\)\uc774\ub77c\uace0 \ud558\uba74 \\(G &#8216; = g\\)\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ubbf8\uc801\ubd84\uc758 \uae30\ubcf8 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[\\int_0^1 x^2 \\,dx = \\int_0^1 g(x) dx = G(1) &#8211; G(0) = \\frac{1}{3} -0 = \\frac{1}{3}\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<\/div>\n<div class=\"remark\">\n<p><span class=\"remark\">\ucc38\uace0.<\/span><br \/>\n\ubbf8\uc801\ubd84\uc758 \uae30\ubcf8 \uc815\ub9ac(\uc815\ub9ac 6.2.2)\uc5d0\uc11c \\(f\\)\uc758 \uc5ed\ub3c4\ud568\uc218 \\(F\\)\ub294 \uc5b4\ub290 \uac83\uc744 \ud0dd\ud558\ub4e0 \uc0c1\uad00 \uc5c6\ub2e4. \uc608\ucee8\ub300 \\(F_1\\)\uc774 \\(f\\)\uc758 \ub610 \ub2e4\ub978 \uc5ed\ub3c4\ud568\uc218\ub77c\uba74 \uc0c1\uc218 \\(C_1\\)\uc774 \uc874\uc7ac\ud558\uc5ec \uc784\uc758\uc758 \\(x\\in [a,\\,b]\\)\uc5d0 \ub300\ud558\uc5ec \\(F(x) = F_1 (x) + C_1\\)\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4. \uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[\\begin{align}<br \/>\n\\int_a^b f(x) dx<br \/>\n&#038;= F(b) &#8211; F(a) \\\\[5pt]<br \/>\n&#038;= (F_1 (b) + C_1 ) &#8211; ( F_1 (a) + C_1 ) \\\\[5pt]<br \/>\n&#038;= F_1 (b) &#8211; F_2 (a)<br \/>\n\\end{align}\\]<br \/>\n\uac00 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n<span class=\"qee\"><\/span><\/p>\n<\/div>\n<p>\ud568\uc218 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(f &#8216; \\)\uc774 \\([a,\\,b]\\)\uc5d0\uc11c \uc801\ubd84 \uac00\ub2a5\ud558\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(x_i\\)\uac00<\/p>\n<p>\\[a = x_0 < x_1 < x_2 < \\cdots < x_{i-1} < x_i < \\cdots < x_{n-1} < x_n = b\\]\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \\((n+1)\\)\uac1c\uc758 \uc810\uc774\ub77c\uace0 \ud558\uc790. \uc774 \uc810\ub4e4\uc758 \ubaa8\uc784\uc744 \\(P\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \ud3c9\uade0\uac12 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec, \\(i=1,\\,2,\\,\\cdots,\\,n\\)\uc77c \ub54c \\(x_{i-1}\\)\uacfc \\(x_i\\) \uc0ac\uc774\uc5d0 \uc810 \\(c_i\\)\uac00 \uc874\uc7ac\ud558\uc5ec \ub2e4\uc74c\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4.\n\\[f ' (c_i ) = \\frac{f(x_i ) - f(x_{i-1})}{x_i - x_{i-1}} .\\]\n\uc774 \uc2dd\uc744 \ubcc0\ud615\ud558\uba74\n\\[f(x_i ) - f(x_{i-1}) = f ' (c_i ) \\Delta x_i\\]\n\uc774\ub2e4. \\(i=1\\)\uc77c \ub54c\ubd80\ud130 \\(i=n\\)\uc77c \ub54c\uae4c\uc9c0 \uc704 \uc2dd\uc744 \ubcc0\ub9c8\ub2e4 \ub354\ud558\uba74\n\\[f(b) - f(a) = \\sum_{i=1}^n f ' (c_i ) \\Delta x_i\\]\n\ub97c \uc5bb\ub294\ub2e4. \\(f ' \\)\uc774 \\([a,\\,b]\\)\uc5d0\uc11c \uc801\ubd84 \uac00\ub2a5\ud558\ubbc0\ub85c \\(\\lVert P \\rVert \\rightarrow 0\\)\uc77c \ub54c \uc704 \ub4f1\uc2dd\uc758 \uc6b0\ubcc0\uc740 \\([a,\\,b]\\)\uc5d0\uc11c \\(f ' \\)\uc758 \uc801\ubd84\uac12\uc5d0 \uc218\ub834\ud55c\ub2e4.<\/p>\n<p>\uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 6.2.3. (\ub3c4\ud568\uc218\uc758 \uc815\uc801\ubd84)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\([a,\\,b]\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(f &#8216; \\)\uc774 \\([a,\\,b]\\)\uc5d0\uc11c \uc801\ubd84 \uac00\ub2a5\ud558\uba74<br \/>\n\\[\\int_a^b f &#8216; (x) dx = f(b)-f(a)\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<\/div>\n<div class=\"remark\">\n<p><span class=\"remark\">\ucc38\uace0.<\/span><br \/>\n\ud568\uc218 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud560\uc9c0\ub77c\ub3c4 \\(f &#8216; \\)\uc740 \\([a,\\,b]\\)\uc5d0\uc11c \uc801\ubd84 \uac00\ub2a5\ud558\uc9c0 \uc54a\uc744 \uc218 \uc788\ub2e4. \uc608\ucee8\ub300 \ud568\uc218 \\(f\\)\uac00 \\([-1,\\,1]\\)\uc5d0\uc11c \ub2e4\uc74c\uacfc \uac19\uc774 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.<br \/>\n\\[f(x) = \\begin{cases}<br \/>\nx^2 \\sin\\frac{1}{x^3} \\quad &#038;\\text{if} \\,\\, x\\ne 0 , \\\\[5pt]<br \/>\n0 \\quad &#038;\\text{if} \\,\\, x =0.<br \/>\n\\end{cases}\\]<br \/>\n\uadf8\ub7ec\uba74<br \/>\n\\[f &#8216; (x) = \\begin{cases}<br \/>\n2x\\sin\\frac{1}{x^3} &#8211; \\frac{3}{x^3} \\cos\\frac{1}{x^3} \\quad &#038;\\text{if} \\,\\, x\\ne 0 , \\\\[5pt]<br \/>\n0 \\quad &#038;\\text{if} \\,\\, x=0<br \/>\n\\end{cases}\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(f &#8216; \\)\uc740 \\(0\\)\uc744 \uc6d0\uc18c\ub85c \uac16\ub294 \uad6c\uac04\uc5d0\uc11c \uc720\uacc4\uac00 \uc544\ub2c8\ub2e4.<\/p>\n<p>\uadf8\ub7ec\ubbc0\ub85c \\(f &#8216; \\)\uc740 \\([-1,\\,1]\\)\uc5d0\uc11c \uc801\ubd84 \ubd88\uac00\ub2a5\ud558\ub2e4.<br \/>\n<span class=\"qee\"><\/span><\/p>\n<\/div>\n<p><!-- ##################################################################### --><br \/>\n<!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n\n\n\n<p>.<\/p>\n\n\n\n\n\n<p>.<\/p>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\u201c\u201d\n\u2018\u2019\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/definite-integrals\">\uc815\uc801\ubd84<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/integral-formulas\">\uc801\ubd84 \uacf5\uc2dd<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 6\uc7a5 2\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) 7\uc7a5 1\uc808\uc5d0\uc11c \uc815\uc801\ubd84\uc744 \uc815\uc758\ud558\uace0 \uc5b4\ub5a0\ud55c \ud568\uc218\uac00 \uc801\ubd84 \uac00\ub2a5\ud55c\uc9c0 \uc0b4\ud3b4\ubcf4\uc558\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \uc815\uc801\ubd84\uc744 \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc744 \uc0b4\ud3b4\ubcf4\uc790. \\(a < b\\)\uc774\uace0 \\(f\\)\uac00 \\(I=[a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc5f0\uc18d\uc778 \uc2e4\uc22b\uac12 \ud568\uc218\ub77c\uace0 \ud558\uc790. \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec \\(G(x) = \\int_a^x f(t) dt\\) \ub77c\uace0 \ud558\uc790. \uc774\uc81c \\(a\\le x < b\\)\ub77c\uace0 \ud558\uace0 \\(\\Delta x\\)\uac00 \\(a < x + \\Delta x \\le b\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc791\uc740&hellip;\n<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":702,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-6735","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6735","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6735"}],"version-history":[{"count":19,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6735\/revisions"}],"predecessor-version":[{"id":8378,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6735\/revisions\/8378"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}