∫上2下1是什么意思
∫代表的是积分上限为2,下限为1的定积分号．绛旓細浠ヨ嚜鐒舵暟e涓哄簳 2鐨勫鏁 ln2
绛旓細骞朵笖鏄棴鏇茬嚎涓婄殑绉垎銆绗簩涓疮鍔犲彿鍙鏅撳緱瀹氫箟灏卞彲浠ユ槑鐧斤紝绗笁涓笉瀹氱Н鍒嗛渶瑕佹湁瀵兼暟鍜屽井鍒嗙殑鍩虹锛屾眰涓嶅畾绉垎涓庢眰瀵兼槸浜掗嗙殑杩囩▼锛屾瘮濡倄^2鐨勫鏁版槸2x锛2x鐨勪笉瀹氱Н鍒嗘槸x^2+C(C涓轰换鎰忓父鏁)锛涜嚦浜庢洸绾跨Н鍒嗚寮勬噦鐨勮瘽锛岄渶瑕佸ぇ閲忕殑寰Н鍒嗙煡璇嗭紝涓嶆槸涓涓嬪氨鑳借窡浣犺娓呮鐨勩
绛旓細涓婇檺浜鍒嗕箣涓鍐欏湪璇ョ鍙峰彸涓婅锛屼笅闄愰浂鍐欏湪璇ョ鍙峰彸涓嬭锛屼唬琛ㄨ鍑芥暟鍦0鍒颁簩鍒嗕箣涓涔嬮棿鐨勭Н鍒嗐
绛旓細鍘熸潵鐨勭Н鍒嗘搴忥紝涓娆℃у湴鍖呮嫭浜嗙矇绾㈣壊閮ㄥ垎璺熻崏缁胯壊閮ㄥ垎锛涗氦鎹㈢Н鍒嗘搴忓悗锛岀Н鍒嗗尯鍩熷氨鍙樻垚浜涓閮ㄥ垎 锛 绮夌孩鑹查儴鍒 + 鑽夌豢鑹查儴鍒嗭紱鏋佸潗鏍囩Н鍒嗙殑绉垎娆″簭鐨鎰忔鏄細A銆佸厛瀵 r 绉垎鐨勬剰鎬濓紝涓涓瀬缁忥紝浠庡師鐐瑰皠鍑 r = 0锛屽皠鍒版瀬鍧愭爣鏂圭▼鐨勬洸绾夸笂锛涚劧鍚庤繖涓瀬缁忥紝閫嗘椂閽堟壂杩囩殑瑙掑害锛屽氨鏄哥殑鑼冨洿銆侭...
绛旓細x=1鏄绉垎鐟曠偣鍚 鎵浠鈭笂闈㈡槸1涓嬮潰鏄0 dx/(x-1)璺 鈭笂闈㈡槸2涓嬮潰鏄1 dx/(x-1)鍚屾椂鏀舵暃瀹冩墠鏀舵暃鍚 杩欎笅鐪嬩笅ln(x-1)(鍘熷嚱鏁)鏄笉鏄弧瓒虫敹鏁涙潯浠跺挴 鍙互鐪嬪埌鍦▁= 1鏃跺欏彇姝ｆ棤绌峰惂 鎵浠ュ彂鏁ｅ挴
绛旓細x=1鏄绉垎鐟曠偣鍚 鎵浠鈭笂闈㈡槸1涓嬮潰鏄0 dx/(x-1)璺 鈭笂闈㈡槸2涓嬮潰鏄1 dx/(x-1)鍚屾椂鏀舵暃瀹冩墠鏀舵暃鍚 杩欎笅鐪嬩笅ln(x-1)(鍘熷嚱鏁)鏄笉鏄弧瓒虫敹鏁涙潯浠跺挴 鍙互鐪嬪埌鍦▁= 1鏃跺欏彇姝ｆ棤绌峰惂 鎵浠ュ彂鏁ｅ挴
绛旓細= 鈭紙鍦ㄤ笂1 ,鍦ㄤ笅0锛1/锛坹锛塣2 d(y-1)= 鈭紙鍦涓2 ,鍦涓1锛1/锛坹锛塣2 dy 锛堝洜涓篸(y-1) / dy = 1锛 鍚屾椂娉ㄦ剰绉垎涓婁笅鍊艰鎹㈡垚y瀵瑰簲鐨勩傦級= (-1 / y) |锛堝湪涓2 ,鍦ㄤ笅1锛 锛堟敞鎰忓埌d(1/y) = -1/y^2锛= (-1/2) - (-1/1)= 1/2 涓棿鏈鍏抽敭鐨勯偅...
绛旓細鈭紙x+1锛夛紙x-2锛塪x=鈭玿²-x-2dx=1/3x³-1/2x²-2x+c 甯﹀叆涓婁笅闄 鍘熷紡=8/3-2-4+1/3-1/2+2=3-4-1/2=-1.5 甯屾湜鑳藉府鍒颁綘锛岃閲囩撼锛岃阿璋
绛旓細瑙ｏ細鈭<-1,2>|x|dx=鈭<0,2>xdx+鈭<-1,0>(-x)dx =(2^2-0^2)/2-(0^2-(-1)^2)/2 =2+1/2 =5/2銆
绛旓細杩欐槸闃朵箻鐨鎰忔锛屾槸涓绉嶆暟瀛﹁繍绠楃鍙凤紝鏄寚浠1涔樹互2涔樹互3涔樹互4涓鐩翠箻鍒扳滐紒鈥濅箣鍓嶇殑鏁般1锛佹槸鎸1鐨勯樁涔橈紝1锛=1锛2锛佹槸鎸2鐨勯樁涔橈紝2锛=1脳2=2锛3锛佹槸鎸3鐨勯樁涔橈紝3锛=1脳2脳3=6锛涗緷娆＄被鎺ㄣ備换浣曞ぇ浜1鐨勮嚜鐒舵暟n闃朵箻琛ㄧず鏂规硶锛 n!=1脳2脳3脳鈥︹γ梟銆傞樁涔樻槸鍩烘柉椤柯峰崱鏇间簬1808骞村彂鏄...
