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©OÃD¿n¤À¥Î¨ìûH¤T¨¤¨ç¼Æ¥N´«¨ä¹ê«Y¦³«e´£¡þ°²³]ªº¡Cº¥ý±ø Definite Integral ûH Range/Direction of Integration «Y¦³¤è¦V¦P¼ÆȽd³òªº¡A«Y¥Ñ¡Ð¢°¨ì¡Ï¢°¡A§Ú¦a·Q¥Î¤@Ó¤T¨¤¨ç¼Æ¥h¥N´«ÃD¤¤ªº x¡A§Ú¦a´zûH©OÓ¨ç¼Æø¯à°÷¹HªðÃD¥Ø³]©wûH¤è¦V¡C
¨ãÅ龤Á¿ x ©OÓÅܼƥѡТ°¼W¥[¨ì¡Ï¢°«Y strictly increasing ¡AËݧڦa¥ç¥u¯à¥N´«¤@Ó strictly increasing ûH¨ç¼Æ¡C°ÝÃD´N¾¤³â¡A§Ú¦a·Q¥ÎûH Sin[\theta] «YÓ©P´Á©Ê¨ç¼Æ¡A¤@®É increasing ¤@®É decreasing¡A©Ò¥H§Ú¦an³z¹L³]©w \theta ûH¨úȽd³ò¾¤¥O¨ì Sin[\theta] ¦b©OÓ Range ¤J±«Yªí²{¥X strictly increasing ûH©Ê½è¡C
°Ñ¦Ò¤U Sin[\theta] ûH¹Ï§A·|µo²{²Å¦X±ø¥óûH½d³ò¨ä¹ê¦³¦n¦h¡G¨Ò¦p¤@¯ë±Ð¬ì®Ñ¥ÎûH ¡Ð¢Þ¢ñ/¢±¨ì¡Ï¢Þ¢ñ/¢±¡A¤S©ÎªÌ¡A¢²¢Þ¢ñ/¢±¨ì¡Ï¢´¢Þ¢ñ/¢±¡C¦ýY§A¨úûH½d³ò«Y¥Ñ¢Þ¢ñ/¢±¨ì¢²¢Þ¢ñ/¢±¡AÊ\«Y¬Û¤Ï¡G¤@Ó strictly decreasing ûH Period¡C
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Integrate[ Sqrt[1-x^2], -1, 1]
=Integrate[ Abs[ Cos[ \theta] ] Cos[ \theta], -Pi/2, Pi/2]
=Integrate[ Cos[ \theta] ^2, -Pi/2 Pi/2]
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Integrate[ Sqrt[1-x^2], -1, 1]
=Integrate[ Abs[ Cos[ \theta] ] Cos[ \theta], 3Pi/2, Pi/2]
=Integrate[ - Cos[ \theta] ^2, 3Pi/2 Pi/2]
= - Integrate[ Cos[ \theta] ^2, 3Pi/2, Pi/2]
¦b©OÓrange ¤J± Cos[ \theta]¡@«Yt¼Æ¡A²Ä¤@Ó Cos[ \theta] ¨úµ´¹ïÈn¥[t¸¹¥ý啱¡C
§A¥i¯àø«Y¦h¥ªÓt¡A«Y¤Ö¥ªÓt¡Att±o¥¿¥ý«Y¥¿½Tµª®×¡C
§Q¥Ó¡G¦n@µLp¼Æ¡A§Æ±æ§ÚûH·§©ÀµL¿ù¡C¡]¦ù脷¡^
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