用二重积分求旋转体的体积

Calculates volume of revolving body with double integral

在微积分中,平面图形绕x轴或y轴旋转所成旋转体的体积用定积分计算已经解决,对于平面图形绕任意直线旋转所成的旋转体的体积如果仍用定积分计算则比较复杂.通过微元法讨论如何用二重积分计算平面图形绕任意不穿过其内部的共面直线旋转一周所成旋转体的体积的一般方法,进而得出一般积分公式.

In the fluxionary calculus, the volume of revolving body formed spinning around x - axis or y - axis by the plane figure became with the definite integral computation already to solve, regarding the volume of revolving body circled the free straight line rotation by the plane figure becomes if still used the definite integral to calculate then quite was complex. This article discuss how to calculate volume of revolving body formed the plane figure to circle willfully the straight line did not pass through its interior to revolve a week, through the element analytic method and the use double integral, then obtains the general integral formula.