定积分求旋转体的体积
1个回答
展开全部
y^2=2x (1)
y=x-4 (2)
sub (2) into (1)
y^2= 2(4+y)
y^2 -2y-8=0
(y-4)(y+2)=0
y=4 or -2
Vy
=π.∫(-2->4) [ (4+y)^2 - (y^2/2)^2 ] dy
=π.∫(-2->4) [ 16+8y +y^2 - (1/4)y^4 ] dy
=π [ 16y+4y^2 +(1/3)y^3 - (1/20)y^5 ]|(-2->4)
=π [ ( 64+64 +64/3 - 256/5 ) -( -32+16-8/3 +8/5) ]
=π [ 144 +72/3 -264/5 ]
=(576/5)π
y=x-4 (2)
sub (2) into (1)
y^2= 2(4+y)
y^2 -2y-8=0
(y-4)(y+2)=0
y=4 or -2
Vy
=π.∫(-2->4) [ (4+y)^2 - (y^2/2)^2 ] dy
=π.∫(-2->4) [ 16+8y +y^2 - (1/4)y^4 ] dy
=π [ 16y+4y^2 +(1/3)y^3 - (1/20)y^5 ]|(-2->4)
=π [ ( 64+64 +64/3 - 256/5 ) -( -32+16-8/3 +8/5) ]
=π [ 144 +72/3 -264/5 ]
=(576/5)π
本回答被网友采纳
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
