高等数学(2版-建工类)定积分的微元法-平面图形的面积-课件.ppt

1、1A)(xfy baxxfA d)()(xfy)0)(xf)(xfy 2，iiixfA )(1iiixx，.)(1iinixfA 01lim()niiiAfx ()dbaf xx,iA niiAA1iA ix，,1iixx 3ab xyo)(xfy xxfAd)(lim.d)(baxxfAd面积元素面积元素 AAxxfAd)(,x ,Ad，xxfAdd)(AAd A,xxxd Ad，xxfd)(xxxd 4()dUf xx ，,xxxd U dx()f x ()dbaf xx 5.d)(baxxfU，,xxxd；xxfUd)(d 6 baxxfAd)(baoyxxx x)(xfy)(xfy，)

2、(xfy),(xgy,bxa )()(xgxf xaboyxxx )(xgy)(xfy，xxgxfAd)()(d baxxgxfA d)()(7 dcyyA d)(dcyx d dcyyyA d)()()(yx ，)(yx ),(yx ,dyc )()(yy ，yyyAd)()(d xoy)(yx )(yx cdxyocd)(yx y+dyyy+dyy8xxfAd)(d xxfAd)(d xxfAd)(d ba)(xfy oabxyx x+dxx+dxx)(xf0)(.1xf0)(.2xf.d baxyxxfd)(A9，)1,1()0,0(xxxAdd)(2 x1,0 xxxxd)(2 103

3、33223 xx.31 2xy 2yx xy 22xy xx+dxx 1 0 A102xy 2yx )1,1()0,0(，yyyAd)(d2 1,0 yy10333223 yy.31 yyyd)(2 1 0 Ayyd y116003)cos(cos xx 可直接从几何可直接从几何意义上得到意义上得到.233 xy=sinxoy3 6 6,3 xx 63sin xxAd 03sin xxd 03sin xxd 60sin xxd 60sin xxd12).4,8(),2,2(422xyxyxy22 4 xyx8,22,0 xxxxAd)2(220 8 2 d)4(2xxxxy22 4 xy.18

4、 xy22 4 xy13y,4,2 yyyyA)d24(d2 4 2dAA xy22 4 xyyyyd)24(4 2 2 xy22 4 xy4 xyxy22.18 14 )()(tytx .)()(21 tttttA d babaxyxxfAdd)(1t2t,21tt,12tt)(tx )(ty 15 tbytaxsincos axyA0d4 02)cos(dsin4 tatbttabdsin4202 .ab 12222 byax1621d()d2Ar ，21()d.2Ar 221rA 圆圆扇扇形形的的面面积积为为()rr 、()r,()0.r ()r r ，,d ，xod d 17.232a

5、 222212 aA2(12sinsin)d 231sin224a 2 d 22)sin1(21d aA2(1sin)d 222 a2 222 a2(1sin)d 183cosr 解解 2232 0 3112(1cos)d(3cos)d22A 1cosr 23x1 cosr 3cosr 3(,)2 3.3(,)23.3cos,1cosrr 得交点坐标为：得交点坐标为：3 3(,),(,),2 323AB 19 2232 0 3112(1cos)d(3cos)d22A 2232 0 31(12coscos)d(3cos)d2 320331992sinsin2sin22424 5.4 20.d)(baxxfU，,xxx ；xxfUd)(d 作图作图21 baxxfAd)(baxx x)(xfy xaboy)(xgy)(xfy baxxgxfA d)()(22xyoy+dyy)(yx cd dcyyAd)(dcyxdxoyy+dyy)(yx )(yx cd dcyyyA d)()(