sinx的平方乘以cosx的三次方 求积分 求sinx的平方乘以cosx的四次方的积分
sinx\u7684\u5e73\u65b9\u4e58cosx3\u6b21\u65b9\u7684\u4e0d\u5b9a\u79ef\u5206 \u662f\u591a\u5c11\uff1f\u5e0c\u671b\u6709\u5177\u4f53\u6b65\u9aa4\u89e3\u9898\u8fc7\u7a0b\u5982\u4e0b\u56fe\uff1a
\u8bb0\u4f5c\u222bf(x)dx\u6216\u8005\u222bf\uff08\u9ad8\u7b49\u5fae\u79ef\u5206\u4e2d\u5e38\u7701\u53bbdx\uff09\uff0c\u5373\u222bf(x)dx=F(x)+C\u3002\u5176\u4e2d\u222b\u53eb\u505a\u79ef\u5206\u53f7\uff0cf(x)\u53eb\u505a\u88ab\u79ef\u51fd\u6570\uff0cx\u53eb\u505a\u79ef\u5206\u53d8\u91cf\uff0cf(x)dx\u53eb\u505a\u88ab\u79ef\u5f0f\uff0cC\u53eb\u505a\u79ef\u5206\u5e38\u6570\u6216\u79ef\u5206\u5e38\u91cf\uff0c\u6c42\u5df2\u77e5\u51fd\u6570\u7684\u4e0d\u5b9a\u79ef\u5206\u7684\u8fc7\u7a0b\u53eb\u505a\u5bf9\u8fd9\u4e2a\u51fd\u6570\u8fdb\u884c\u4e0d\u5b9a\u79ef\u5206\u3002
\u6269\u5c55\u8d44\u6599\u5e38\u7528\u79ef\u5206\u516c\u5f0f\uff1a
1\uff09\u222b0dx=c
2\uff09\u222bx^udx=(x^(u+1))/(u+1)+c
3\uff09\u222b1/xdx=ln|x|+c
4\uff09\u222ba^xdx=(a^x)/lna+c
5\uff09\u222be^xdx=e^x+c
6\uff09\u222bsinxdx=-cosx+c
7\uff09\u222bcosxdx=sinx+c
8\uff09\u222b1/(cosx)^2dx=tanx+c
\u5177\u4f53\u56de\u7b54\u5982\u56fe\uff1a
\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u5b9e\u6570x\u90fd\u5bf9\u5e94\u7740\u552f\u4e00\u7684\u89d2\uff08\u5f27\u5ea6\u5236\u4e2d\u7b49\u4e8e\u8fd9\u4e2a\u5b9e\u6570\uff09\uff0c\u800c\u8fd9\u4e2a\u89d2\u53c8\u5bf9\u5e94\u7740\u552f\u4e00\u786e\u5b9a\u7684\u6b63\u5f26\u503csinx\uff0c\u8fd9\u6837\uff0c\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u5b9e\u6570x\u90fd\u6709\u552f\u4e00\u786e\u5b9a\u7684\u503csinx\u4e0e\u5b83\u5bf9\u5e94\uff0c\u6309\u7167\u8fd9\u4e2a\u5bf9\u5e94\u6cd5\u5219\u6240\u5efa\u7acb\u7684\u51fd\u6570\uff0c\u8868\u793a\u4e3ay=sinx\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u8fde\u7eed\u51fd\u6570\uff0c\u4e00\u5b9a\u5b58\u5728\u5b9a\u79ef\u5206\u548c\u4e0d\u5b9a\u79ef\u5206\uff1b\u82e5\u5728\u6709\u9650\u533a\u95f4[a,b]\u4e0a\u53ea\u6709\u6709\u9650\u4e2a\u95f4\u65ad\u70b9\u4e14\u51fd\u6570\u6709\u754c\uff0c\u5219\u5b9a\u79ef\u5206\u5b58\u5728\uff1b\u82e5\u6709\u8df3\u8dc3\u3001\u53ef\u53bb\u3001\u65e0\u7a77\u95f4\u65ad\u70b9\uff0c\u5219\u539f\u51fd\u6570\u4e00\u5b9a\u4e0d\u5b58\u5728\uff0c\u5373\u4e0d\u5b9a\u79ef\u5206\u4e00\u5b9a\u4e0d\u5b58\u5728\u3002
\u5c06\u6240\u6c42\u79ef\u5206\u5316\u4e3a\u4e24\u4e2a\u79ef\u5206\u4e4b\u5dee\uff0c\u79ef\u5206\u5bb9\u6613\u8005\u5148\u79ef\u5206\u3002\u5b9e\u9645\u4e0a\u662f\u4e24\u6b21\u79ef\u5206\u3002
\u6709\u7406\u51fd\u6570\u5206\u4e3a\u6574\u5f0f\uff08\u5373\u591a\u9879\u5f0f\uff09\u548c\u5206\u5f0f\uff08\u5373\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u5546\uff09\uff0c\u5206\u5f0f\u5206\u4e3a\u771f\u5206\u5f0f\u548c\u5047\u5206\u5f0f\uff0c\u800c\u5047\u5206\u5f0f\u7ecf\u8fc7\u591a\u9879\u5f0f\u9664\u6cd5\u53ef\u4ee5\u8f6c\u5316\u6210\u4e00\u4e2a\u6574\u5f0f\u548c\u4e00\u4e2a\u771f\u5206\u5f0f\u7684\u548c\uff0e\u53ef\u89c1\u95ee\u9898\u8f6c\u5316\u4e3a\u8ba1\u7b97\u771f\u5206\u5f0f\u7684\u79ef\u5206\uff0e
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u4e0d\u5b9a\u79ef\u5206
绛旓細鎸夋垜鐨勭洿瑙夋潵璇 搴旇鏄繖鏍
绛旓細鍏堟彁鍑簊inx鐨勫钩鏂瑰氨鍙樻垚鏍瑰彿涓媠inx鐨勫钩鏂逛箻浠ユ嫭鍙(1-sinx鐨勫钩鏂)锛岃1-sinx鐨勫钩鏂瑰氨绛変簬cosx鐨勫钩鏂广 灏卞彉鎴愪簡鏍瑰彿涓sinx鐨勫钩鏂逛箻浠osx鐨骞虫柟锛佸紑鏂逛互鍚庡氨鎴愪簡sinxcosx浜嗭紒锛侊紒鍔犳补锛佸姞娌瑰惂锛侀獨骞达紒锛侊紒
绛旓細sin²xcos²x=1/4sin²2x銆傚垎鏋愯繃绋嬪涓嬶細sin²xcos²x =锛sinxcosx锛²=锛1/2脳2sinxcosx锛²=锛1/2sin2x锛²=1/4sin²2x
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細杩欎釜搴旇绠鍗 涔︽湰涓婃湁绫讳技鐨勪緥棰橈紝鎼炴竻妤氬彉鍖栬繃绋嬪氨琛岋紒O(鈭鈭)O~锛
绛旓細浜屽嶈鍏紡sinx涔樹互cosx=1/2*sin2x 鎵浠in^2 *x 涔樹互cos^2*x= 1/4sin^2*2x 瀵筬(x)=1/4sin^2*2x姹傚鏄鍚堝嚱鏁版眰瀵煎彟u=sinv锛寁=2x锛屾墍浠锛坸锛=1/2u^2锛屽鍚堝嚱鏁版眰瀵兼硶鍒欏氨琛屼簡銆傝繖鏄眰瀵奸噷闈㈡渶鍩虹鐨勩傚缓璁湅鐪嬩功
绛旓細濡傛灉鏄cosxdx鐨勮瘽锛岄偅涔堝氨鏄痗osxdx = dsinx 鎶妔inx鐪嬫垚t
绛旓細鍥炵瓟锛氫笂涓嬪悓鏃涔樹互cosx,鐒跺悗涓婅竟鐨刢os,鍙互鏀惧埌鍚庤竟鍘,鐒跺悗涓婅竟鏄1-cos^2x,涓嬭竟鏄痗os^4x,鍙互鎹㈠厓浜,鐒跺悗鎷嗘垚涓や釜,杩欎箞澶氭彁绀哄浜嗗惂
绛旓細杩欐牱銆傚洜涓篴bc<=((a+b+c)/3)^3 (sinx)^2*(cosx)^4 =1/2*(2*(sinx)^2)*(cosx)^2* (cosx)^2 <=1/2*((2*(sinx)^2)+(cosx)^2+ (cosx)^2)/3)^3 =4/27 姝ゆ椂 (sinx)^2锛1/3 鍏跺疄锛屼綘鍙互鍙傝僪ttp://zhidao.baidu.com/question/16197348.html 閭ｆ槸涓涓緢濂界殑棰樼洰銆
绛旓細璇卞鍏紡锛歴in锛埾/2+x锛=cosx锛宑os锛埾/2+x锛=鈥sinx銆傝瘉鏄庯細sinx鈭2+cosx鈭2=1锛岀Щ椤瑰緱sinx鈭2=1-cosx鈭2锛屽紑骞虫柟寰梥inx=卤鈭氾紙1-cosx鈭2锛夈傚悓鐞唖inx鈭2+cosx鈭2=1锛岀Щ椤瑰緱cosx鈭2=1-sinx鈭2锛屽紑骞虫柟寰梒osx=卤鈭氾紙1-sinx鈭2锛夈2鍊嶈鍙樻崲鍏崇郴 浜屽嶈鍏紡閫氳繃瑙捨辩殑涓夎鍑芥暟鍊...
