sin平方x的积分是什么?
sin平方x的积分= 1/2 X -1/4 sin2X + C。
解:∫(sinx)^2dx=(1/2)∫(1-cos2x)dx=(1/2)x-(1/4)sin2x+C(C为常数)。
不定积分的公式
1、∫ a dx = ax + C,a和C都是常数
2、∫ x^a dx = [x^(a + 1)]/(a + 1) + C,其中a为常数且 a ≠ -1
3、∫ 1/x dx = ln|x| + C
4、∫ a^x dx = (1/lna)a^x + C,其中a > 0 且 a ≠ 1
5、∫ e^x dx = e^x + C
6、∫ cosx dx = sinx + C
7、∫ sinx dx = - cosx + C
8、∫ cotx dx = ln|sinx| + C = - ln|cscx| + C
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細sin骞虫柟x鐨勭Н鍒= 1/2x -1/4 sin2x + C(C涓哄父鏁)銆傝В绛旇繃绋嬪涓嬶細瑙o細鈭(sinx)^2dx =(1/2)鈭(1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁)
绛旓細sin骞虫柟x鐨勭Н鍒= 1/2 X -1/4 sin2X + C 瑙:鈭(sinx)^2dx=(1/2)鈭(1-cos2x)dx=(1/2)x-(1/4)sin2x+C(C涓哄父鏁)濡傛灉涓涓嚱鏁癴鍦ㄦ煇涓尯闂翠笂榛庢浖鍙Н锛屽苟涓斿湪姝ゅ尯闂翠笂澶т簬绛変簬闆躲傞偅涔堝畠鍦ㄨ繖涓尯闂翠笂鐨勭Н鍒嗕篃澶т簬绛変簬闆躲傚鏋渇鍕掕礉鏍煎彲绉苟涓斿嚑涔庢绘槸澶т簬绛変簬闆讹紝閭d箞瀹冪殑鍕掕礉鏍肩Н鍒...
绛旓細sin骞虫柟x鐨勭Н鍒= 1/2x -1/4 sin2x + C(C涓哄父鏁)銆傝В绛旇繃绋嬪涓嬶細瑙o細鈭紙sinx)^2dx =(1/2)鈭紙1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁帮級鍩烘湰浠嬬粛 绉垎鍙戝睍鐨勫姩鍔涙簮鑷疄闄呭簲鐢ㄤ腑鐨勯渶姹傘傚疄闄呮搷浣滀腑锛屾湁鏃跺欏彲浠ョ敤绮楃暐鐨勬柟寮忚繘琛屼及绠椾竴浜涙湭鐭ラ噺锛屼絾闅忕潃绉戞妧鐨勫彂灞曪紝寰堝鏃跺欓渶瑕佺煡閬...
绛旓細sin骞虫柟x鐨勭Н鍒= 1/2x -1/4 sin2x + C(C涓哄父鏁)銆傝В绛旇繃绋嬪涓嬶細瑙o細鈭(sinx)^2dx =(1/2)鈭(1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁)涓嶅畾绉垎鐨勬剰涔夛細濡傛灉f(x)鍦ㄥ尯闂碔涓婃湁鍘熷嚱鏁帮紝鍗虫湁涓涓嚱鏁癋(x)浣垮浠绘剰x鈭圛锛岄兘鏈塅'(x)=f(x)锛岄偅涔堝浠讳綍甯告暟鏄剧劧涔熸湁[F(x)+...
绛旓細鎶奡IN2 X鍒╃敤浜屽嶈鍏紡鍙互鍖栦綔锛1-COS 2X锛/2锛屽啀杩涜绉垎 sin骞虫柟x鐨勭Н鍒= 1/2x -1/4 sin2x + C(C涓哄父鏁)銆傝В绛旇繃绋嬪涓嬶細瑙o細鈭(sinx)^2dx =(1/2)鈭(1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁)
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細鑻ユ湁甯姪锛岃閲囩撼銆
绛旓細sin骞虫柟x鐨勭Н鍒= 1/2x -1/4 sin2x + C(C涓哄父鏁)銆傝В锛氣埆锛坰inx)^2dx =(1/2)鈭紙1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁帮級鍒嗛儴绉垎锛(uv)'=u'v+uv'寰楋細u'v=(uv)'-uv'涓よ竟绉垎寰楋細鈭玼'v dx=鈭紙uv)' dx -鈭玼v' dx銆傚嵆锛氣埆u'v dx = uv -鈭玼v' d,杩欏氨...
绛旓細sin骞虫柟x鐨勭Н鍒= 1/2x -1/4 sin2x + C(C涓哄父鏁)銆傝В绛旇繃绋嬪涓嬶細瑙o細鈭(sinx)^2dx =(1/2)鈭(1-cos2x)dx =(1/2)x-(1/4)sin2x+C(C涓哄父鏁)瀹氫箟绉垎 鏂规硶涓嶆涓绉嶏紝鍚勭瀹氫箟涔嬮棿涔熶笉鏄畬鍏ㄧ瓑浠风殑銆傚叾涓殑宸埆涓昏鏄湪瀹氫箟鏌愪簺鐗规畩鐨勫嚱鏁帮細鍦ㄦ煇浜涚Н鍒嗙殑瀹氫箟涓嬭繖浜涘嚱鏁颁笉鍙Н鍒嗭紝浣嗗湪...
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