calculus,use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y-axis,y=2+x-x^2, x + y =2V=( ? )

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calculus,use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y-axis,y=2+x-x^2, x + y =2V=( ? )
calculus,
use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y-axis,
y=2+x-x^2, x + y =2
V=( ? )

calculus,use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y-axis,y=2+x-x^2, x + y =2V=( ? )
第一步：联立y=2+x-x^2, x + y =2可以解出来,两曲线的交点为x=0,y=2；x=2,y=0
第二步：由交点可以确定两曲线围成了一个闭合曲线,按题目要求,为这个闭合曲线绕y轴旋转所产生的类圆柱壳的体积,那么用微积分的元素分析法,可以确定圆柱壳的微分表达式,即
dV=2*pi*x*【g(x)-f(x)】dx ,其中g(x)=2+x-x^2,f(x)=2-x
第三步：对上面的圆柱壳微分量在0到2上积分即可求得最后的体积V=(8*pi)/3.

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