定积分的应用（面积）.ppt

2 复习:定积分的几何意义 1A 2A 3A 4A 4321d)(AAAAxxf ba????? Axxfxf ba??? d)(,0)( 曲边梯形面积??? baxxfxfd)(,0)( 曲边梯形面积的负值 A? 3 ab)(xf x y0;??? baxxfAxfd)(,0)( ab )(xfx y0 ;???? baxxfAxfd)(,0)(????.d)(A?? baxxf 4 若 f (x)有正有负,)(?? baxxfA)(xfy?)(xfy?x yoab 5 ;??? bayyAyd)(,0)(?? a b)(yx??x y0 ;???? bayyAyd)(,0)(??.d)(A?? bayy? b)(yx??x y0 a )(yx?? yx b ?a ? 6 y=f(x ), y=g(x ), 直线 x=a, x=b (a<b)所围成的平面图形的面积 c x yoab )(xfy?)(xgy??A??? ca caxxgxxfd)(d)(???? bc bcxxfxxgd)(d)(??? caxxgxfd )]()([??? acxxfxgd )]()([?????? ac caxxgxfxxgxfd)()(d)()(??? baxxgxfd)()( 7 y=f(x ), y=g(x ), 直线 x=a, x=b (a<b)所围成的平面图形的面积 c x yoab )(xfy?)(xgy???? baxxgxfAd)()( 8 特别, 时, )()(xgxf?x yoab )(xfy?)(xgy???? baxxgxfAd )]()([ 9 ,d)(dxxfA?面积元素: 由连续曲线 y = f (x ) ( f (x ) ? 0), 直线 x=a, x=b (a<b) 及x 轴所围成的平面图形的面积)(xfy?b yo xax xx???? baxxfAd)(面积 10 由连续曲线 y=f(x ), y=g(x ), 直线 x=a, x=b (a<b)所围成的平面图形的面积 cx xx?? x yoab )(xfy?)(xgy???? baxxgxfAd)()( ,d)()(dxxgxfA??面积元素: