å¸¦æ ¹å·çå®ç§¯åæ±æ³å¦ä¸ï¼
令x=sint
xï¼0â1ï¼åtï¼0âÏ/2
â«[0ï¼1]â(1-x²)dx
=â«[0ï¼Ï/2]â(1-sin²t)d(sint)
=â«[0ï¼Ï/2]cos²tdt
=½â«[0ï¼Ï/2](1+cos2t)dt
=(½t+¼sin2t)|[0ï¼Ï/2]
=[½Â·(Ï/2)+¼sinÏ]-(½Â·0+¼sin0)
=Ï/4
é»æ¼ç§¯å
å®ç§¯åçæ£å¼å称æ¯é»æ¼ç§¯åãç¨é»æ¼èªå·±çè¯æ¥è¯´ï¼å°±æ¯æç´è§åæ ç³»ä¸çå½æ°çå¾è±¡ç¨å¹³è¡äºyè½´çç´çº¿æå ¶åå²ææ æ°ä¸ªç©å½¢ï¼ç¶åææ个åºé´[a,b]ä¸çç©å½¢ç´¯å èµ·æ¥ï¼æå¾å°çå°±æ¯è¿ä¸ªå½æ°çå¾è±¡å¨åºé´[a,b]çé¢ç§¯ãå®é ä¸ï¼å®ç§¯åçä¸ä¸éå°±æ¯åºé´ç两个端ç¹a,b.
æ们å¯ä»¥çå°ï¼å®ç§¯åçæ¬è´¨æ¯æå¾è±¡æ éç»åï¼åç´¯å èµ·æ¥ï¼è积åçæ¬è´¨æ¯æ±ä¸ä¸ªå¯¼å½æ°çåå½æ°ã