第七章定积分 1,体积 切片 dv=ndx =「x(R2-x2 -R R 4R R 卷筒 dv=2D(2ydx) =|4m√R2-x2dx= -∫2rR2-xR2-x 包锥 d=2丌 2Rsin r2 Isin p do=R 2,球面面积 L=「2m√1+(0)2a △OAB~4pgB,∠pBq=∠OBA b dl d →dl=-ax OB AB R dS=2mdI=2rR dx=S=2 2rRdx=4zR 第七章定积分第七章 定积分 第七章 定积分 1, 体积: ⚫ 切片: dV y dx 2 =  , ( )  − = − R R V R x dx 2 2  = ( )  − R R x dx 0 2 2 2  = 3 4 3 2 3 3 3 R R R =         − ⚫ 卷筒 dV = 2x(2ydx),  = − R V x R x dx 0 2 2 4 = = ( )  − − − R R x d R x 0 2 2 2 2 2 ⚫ 包锥         =    d R R dV 3 2 2 sin 2 2 ,  =     0 3 sin 3 2 d R V = 3 3 4 R 2, 球面面积: ⚫ dS = 2y dl( )  − = +  R R L y y dx 2 2 1 OAB ~ pqB , pBq = OBA dx y R dl y dx R dl AB qB OB pB  =  =  = , dS = 2y dl = 2R dx 2 0 S 2 2 Rdx 4 R R  =  =   . y R x 2 + y2 =R2 -R 0 x x+△x R x -R y R x 2 + y2 =R2 △ -R 0  R y R p x 2 + y2 =R2 q B -R 0 x x+△x R A