正弦函数乘于余弦函数的三次方的原函数？ 余弦函数的三次方的不定积分
\u6b63\u5f26\u51fd\u6570\u4e09\u6b21\u65b9\u7684\u539f\u51fd\u6570\u662f\u591a\u5c11\u6b63\u5f26\u51fd\u6570\u4e09\u6b21\u65b9\u7684\u539f\u51fd\u6570\u662f-cosx+1/3*(cosx)^3+C\u3002
\u89e3\uff1a\u4ee4F(x)\u4e3a(sinx)^3\u7684\u539f\u51fd\u6570\u3002
\u90a3\u4e48F(x)=\u222b(sinx)^3dx
=\u222b(sinx)^2*sinxdx
=-\u222b(1-(cosx)^2)/d(cosx)
=\u222bd(cosx)+1/2\u222b(cosx)^2d(cosx)
=-cosx+1/3*(cosx)^3+C
\u5373(sinx)^3\u7684\u539f\u51fd\u6570\u662f-cosx+1/3*(cosx)^3+C\u3002
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u4e09\u89d2\u51fd\u6570\u516c\u5f0f
(sinA)^2=(1-cos2A)/2\u3001(cosA)^2=(cos2A-1)/2\u3001(sinA)^2+(cosA)^2=1\u3001sin2A=2sinAcosA
2\u3001\u4e0d\u5b9a\u79ef\u5206\u51d1\u5fae\u5206\u6cd5
\u901a\u8fc7\u51d1\u5fae\u5206\uff0c\u6700\u540e\u4f9d\u6258\u4e8e\u67d0\u4e2a\u79ef\u5206\u516c\u5f0f\u3002\u8fdb\u800c\u6c42\u5f97\u539f\u4e0d\u5b9a\u79ef\u5206\u3002
\u4f8b\uff1a\u222bcos3xdx=1/3\u222bcos3xd(3x)=1/3sin3x+C
\u76f4\u63a5\u5229\u7528\u79ef\u5206\u516c\u5f0f\u6c42\u51fa\u4e0d\u5b9a\u79ef\u5206\u3002
3\u3001\u5e38\u7528\u7684\u4e0d\u5b9a\u79ef\u5206\u516c\u5f0f
\u222b1dx=x+C\u3001\u222b1/xdx=ln|x|+C\u3001\u222bcosxdx=sinx+C\u3001\u222bsinxdx=-cosx+C
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u4e0d\u5b9a\u79ef\u5206
\u222b4(cosx)^3dx
=4\u222b(cosx)^2 cosxdx
=4\u222b[1-(sinx)^2]d(sinx)
=4[sinx-(sinx)^3/3]
=8[sin\u03c0/2-(sin\u03c0/2)^3/3]
=8[1-1/3]
=16/3
=-∫cos³xd(cosx)
=-¼cos⁴x+C
绛旓細鍥炵瓟锛氾節0,1/2锕
绛旓細1銆姝ｅ鸡鍑芥暟sin(x)鐨勮繛鍒嗗紡灞曞紑锛歴in(x) = x / (1 + a1^2 x^2 / (1 + a2^2 x^2 / (1 + a3^2 x^2 / ...)))鍏朵腑锛宎n = 2n - 1锛宯涓烘鏁存暟銆2銆浣欏鸡鍑芥暟cos(x)鐨勮繛鍒嗗紡灞曞紑锛歝os(x) = 1 / (a1^2 x^2 / (1 + a2^2 x^2 / (a3^2 x^2 / ...)))鍏...
绛旓細y=xsin(1/x)鐨勫浘鍍忥細绉殑鍏崇郴锛sin伪 = tan伪 脳 cos伪锛堝嵆sin伪 / cos伪 = tan伪 锛塩os伪 = cot伪 脳 sin伪 锛堝嵆cos伪 / sin伪 = cot伪锛塼an伪 = sin伪 脳 sec伪 (鍗 tan伪 / sin伪 = sec伪)
绛旓細2銆佷笁瑙掑嚱鏁扮殑鎬ц川 涓夎鍑芥暟鍏锋湁涓浜涢噸瑕佺殑鎬ц川锛屼緥濡傦細鍛ㄦ湡鎬э細姝ｅ鸡鍜浣欏鸡鍑芥暟鐨鍛ㄦ湡閮芥槸2蟺锛屽嵆瀹冧滑鍦ㄦ瘡闅2蟺鐨勮搴﹂噸澶嶃傛湁鐣屾э細姝ｅ鸡鍜屼綑寮﹀嚱鏁扮殑鍊煎煙閮藉湪-1鍜1涔嬮棿锛屽嵆瀹冧滑鐨勫彇鍊艰寖鍥存槸鏈夌晫鐨勩傚绉版э細姝ｅ鸡鍑芥暟鍦ㄥ绉拌酱澶勫彇鍊间负0锛岃屼綑寮﹀嚱鏁板湪瀵圭О杞村鍙栧间负1鎴-1锛屽嵆瀹冧滑閮藉叿鏈夊绉版с
绛旓細sin2x = 2sinxcosx銆傝В閲婏細鍦ㄤ笁瑙掑嚱鏁伴噷锛屽綋鎴戜滑鎯宠璁＄畻sin2x鏃讹紝鍙互鍒╃敤姝ｅ鸡鐨勪簩鍊嶈鍏紡銆傝繖涓叕寮忓憡璇夋垜浠紝sin2x骞朵笉绛変簬绠鍗曠殑涓ゅ嶆寮﹀嚱鏁皊inx鐨勫硷紝鑰屾槸绛変簬姝ｅ鸡鍑芥暟涔樹互浣欏鸡鍑芥暟鐨浜屽嶈褰㈠紡銆傚叿浣撴潵璇达紝sin2x绛変簬姝ｅ鸡鍑芥暟涔樹互浣欏鸡鍑芥暟鐨勪袱鍊嶏紝涔熷氨鏄敤鍏紡琛ㄧず涓猴細sin2x = 2sinxcosx銆傝繖鏄竴...
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绛旓細sina cosa=1/2sin2a 锛屾墍浠ュ懆鏈熸槸sina 鐨勪竴鍗婏細蟺
绛旓細绛旀濡傚浘
