求由y=sinx(0≤x≤π)与x轴围成的平面图形绕x轴，绕y轴旋转而成的旋转体体积．
绕轴z旋转 υx=π∫0πsin2xdx=π∫0π[(1-cos2x)/2]dx=π2/2 绕轴y旋转 υy=π∫01[(π-arcsiny)2-(arcsin2y)]dy =π∫01(π2-2πarcsiny)dy =π∫0π/2-2πt)costdt=2π2
求由y=sinx(0≤x≤π)与x轴围成的平面图形绕x轴，绕y轴旋转而成的旋转体体积．
绕轴z旋转 υx=π∫0πsin2xdx=π∫0π[(1-cos2x)/2]dx=π2/2 绕轴y旋转 υy=π∫01[(π-arcsiny)2-(arcsin2y)]dy =π∫01(π2-2πarcsiny)dy =π∫0π/2-2πt)costdt=2π2
