更新时间2019-06-09 21:46:09
两抛物线交点 2x^2 = 3 - x^2,x^2 = 1,x = ±1;
y = 3 - x² = 0,零点 x = √3;
旋转体ACE,dv1 = πx^2dy = πx^2 * (4x)dx = 4πx^3dx;
旋转体ABDE,dv2 = πx^2dy = πx^2 * (2x)dx = 2πx^3dx;
所求旋转体体积 V = V2 - V1 = 2π{ ∫( 1,√3 )(x^3)dx - ∫( 0,1 )(x^3)dx
= 2π{ [ x^4/4 ]( 1,√3 ) - [ x^4/4 ]( 0,1 ) ] }
= 2π{ [ 9/4 - 1/4 ] - [ 1/4 ] }
= 7π/2 。
图呢?请提供图