求解用积分求旋转体体积题（2条线相交,绕y=-1旋转.r加一还是2还是4搞不清了--）LetRbetheregionintheplaneboundedbythey=x,y=x^2,x=2(soRismadeof2partsR由两部分组成).\x05\x05\x05Findthevolumeoftheso

Question

求解用积分求旋转体体积题（2条线相交,绕y=-1旋转.r加一还是2还是4搞不清了- -）
Let R be the region in the plane bounded by the y=x,y=x^2,x=2
(so R is made of 2 parts R由两部分组成).
\x05\x05\x05
Find the volume of the solid of revolution obtained by rotating R around the
line y = −1.
这两部分绕着y=-1旋转,求旋转体体积.

Answer 1

先把y=x,y=x^2,x=2三条曲线的交点求到,总共有四个交点：(0,0),(1,1),(2,2),(2,4),以x作为积分变量,每个积分微元dx对应的是一个圆环(薄片）,其体积为：dV ＝ | π (x+1)^2 － π(x^2+1)^2 | dxV ＝ ∫(0,2) | π (x+1...