{"id":402,"date":"2025-10-11T14:56:36","date_gmt":"2025-10-11T14:56:36","guid":{"rendered":"http:\/\/saegil-lab.kr\/?p=402"},"modified":"2025-10-23T05:47:09","modified_gmt":"2025-10-23T05:47:09","slug":"latexpage-%ec%9b%90%ec%9d%98-%eb%a9%b4%ec%a0%81-spi-r2-%ec%a6%9d%eb%aa%85-2","status":"publish","type":"post","link":"https:\/\/saegil-lab.kr\/?p=402","title":{"rendered":"\uc6d0\uc758 \uba74\uc801 \"S=\pi r^2\" \uc99d\uba85 2"},"content":{"rendered":"\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

\uc911\uc2ec\uc774 \uc6d0\uc810\uc778 \uc6d0\uc5d0 \ub300\ud574 1\uc0ac\ubd84\uba74\uc758 \uba74\uc801 \"S_1\"\uc744 \uad6c\ud558\uace0 4\ubc30\ub97c \ud574\uc11c \uc6d0\uc758 \uba74\uc801\uc744 \uad6c\ud55c\ub2e4.<\/p>\n\n\n\n

\uc6d0\uc810\uc744 \uc911\uc2ec\uc73c\ub85c \ud558\ub294 \uc6d0\uc758 \ubc29\uc815\uc2dd\uc740 \"x^2 + y^2 = r^2\" \uc774\ubbc0\ub85c \"x\"\uc77c \ub54c\uc758 \"y\"\uac12\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ y=\sqrt{r^2 - x^2} \]\"<\/p><\/p>\n\n\n\n

1\uc0ac\ubd84\uc5d0\uc11c \uba74\uc801 \uc694\uc18c \"dS_1\"\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ dS_1 = y dx = \sqrt{r^2-x^2} dx \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \therefore S_1 = \int_0^r \sqrt{r^2 - x^2} dx \]\"<\/p><\/p>\n\n\n\n

\"x = r \cos\theta\"\ub77c\uace0 \ud558\uba74 \"x=0\"\uc77c \ub54c \"\theta= \frac{\pi}{2}\", \"x=r\"\uc77c \ub54c \"\theta=0\"\uc774 \ub418\ub294 \uac83\uc744 \uc54c \uc218 \uc788\uace0 \ub2e4\uc74c\uacfc \uac19\uc740 \uad00\uacc4\ub97c \ucc3e\uc744 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ dx = -r \sin \theta d\theta \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \sqrt{r^2 - x^2} = r \sin \theta \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \therefore S_1 = \int_{\frac{\pi}{2}}^{0} r \sin \theta (- r \sin \theta) d\theta = \int_0^{\frac{\pi}{2}} r^2 \sin^2\theta d\theta\]\"<\/p><\/p>\n\n\n\n

\"\cos 2\theta = 1- 2 \sin^2 \theta\"\ub77c\ub294 \uad00\uacc4\uac00 \uc131\ub9bd\ud558\ubbc0\ub85c <\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ S_1 = r^2\int_0^{\frac{\pi}{2}} \frac{1 - \cos 2\theta}{2} d\theta = \frac{r^2}{2} \left[ \theta - \frac{1}{2} \sin 2 \theta \right] _0^{\frac{\pi}{2}} = \frac{1}{4}\pi r^2 \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\therefore S = 4S' = 4 \cdot \frac{1}{4} \pi r^2 = \pi r^2 \]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \]\"<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

\uc911\uc2ec\uc774 \uc6d0\uc810\uc778 \uc6d0\uc5d0 \ub300\ud574 1\uc0ac\ubd84\uba74\uc758 \uba74\uc801 \uc744 \uad6c\ud558\uace0 4\ubc30\ub97c \ud574\uc11c \uc6d0\uc758 \uba74\uc801\uc744 \uad6c\ud55c\ub2e4. \uc6d0\uc810\uc744 \uc911\uc2ec\uc73c\ub85c \ud558\ub294 \uc6d0\uc758 \ubc29\uc815\uc2dd\uc740 \uc774\ubbc0\ub85c \uc77c \ub54c\uc758 \uac12\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.     1\uc0ac\ubd84\uc5d0\uc11c \uba74\uc801 \uc694\uc18c \uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.         … \uacc4\uc18d \uc77d\uae30 →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[21,20,19,18,25,14],"class_list":["post-402","post","type-post","status-publish","format-standard","hentry","category-13","tag-pi","tag-pi-r2","tag-19","tag-18","tag-25","tag-14"],"_links":{"self":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/402","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=402"}],"version-history":[{"count":11,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/402\/revisions"}],"predecessor-version":[{"id":611,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/402\/revisions\/611"}],"wp:attachment":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}