(1)直线x=2与曲线y=x^3交点坐标是(2,8)绕OX轴旋转一周的体积是V1=∫(0,2)π(x^3)^2dx=∫(0,2)πx^6dx=πx^7/7|(0,2)=128π/7绕OY轴旋转一周的体积V2=π*2^2*8-∫(0,8)πx^2dy=32π-∫(0,8)πy^(2/3）dy=32π-3π/5*y^(5/3)|(0,8)=64π/5(2)旋转体的体积等于上半部分旋转体体积的2倍V=2∫(0,R)π[(x+b)^2-(-x+b)^2]dy =8bπ∫(0,R)xdy令x=Rcosa,y=Rsina,(a∈[0,π/2])V=8bπ∫(0,π/2)Rcosa*...
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