微积分数学题,求体积.find the volume of the solid whose base is the region bounded by y=x^4,y=1,and the y-axis and whose cross-sections perpendicular to the y-axis are equilateral triangles.volume=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 09:48:42

微积分数学题,求体积.find the volume of the solid whose base is the region bounded by y=x^4,y=1,and the y-axis and whose cross-sections perpendicular to the y-axis are equilateral triangles.volume=?
微积分数学题,求体积.
find the volume of the solid whose base is the region bounded by y=x^4,y=1,and the y-axis and whose cross-sections perpendicular to the y-axis are equilateral triangles.
volume=?

微积分数学题,求体积.find the volume of the solid whose base is the region bounded by y=x^4,y=1,and the y-axis and whose cross-sections perpendicular to the y-axis are equilateral triangles.volume=?

体积是√3/6.



跟着y坐标,等边三角形的边长是x=y^(1/4),因此截面积为S=√3/4*(y^(1/4))^2=√3/4*√y,


然后把这个式子对y从0到1积分,得原函数√3/6 * y^(3/2),把端点0和1代进去,得V=√3/6.


下面是根据本人对题意理解,还原的三维效果图.

微积分数学题,求体积find the volume of the solid whose base is the region bounded by y=x^4,y=1,and the y-axis and whose cross-sections perpendicular to the x-axis are semicircles.volume=? 微积分数学题,求体积.find the volume of the solid whose base is the region bounded by y=x^4,y=1,and the y-axis and whose cross-sections perpendicular to the y-axis are equilateral triangles.volume=? 微积分高等数学题 求极限 数学微积分中的积分 求旋转的体积 只要答案即可 Find the volume of the solid obtained by rotating the region bounded by y=x^2,y=0,x=5,and about the y-axis.求绕y轴旋转后的体积.Find the volume of the solid formed by rotatin 求微积分题高等数学题求过程 微积分数学题/> 数学题微积分 微积分数学题 微积分题 高等数学题求极限 一道数学题,用到初级微积分A right circular cylinder is inscribed in a sphere of radius r.Find the lagest possible surface area of such a cylinder. 微积分:求极限Find the limit.lim x→ 无穷大(e^−7x cos x) 高数微积分求体积Let R be the region {(x,y): 0 高数微积分体积Vy怎么求 数学微积分求体积题目如图 f(x)=2cosx 求这个题目的微积分原体是怎么写的:Find the derivativesf(x)=2cosx 简单的微积分数学题一道求曲线周长,如图, 求一道微积分的数学题百度空间相册有题 Alevel微积分数学题请求老师同学解答/1,Find the general solution of the equationdy/dx=tanxcotydy/dx=y(y-1)/x (1,2)dy/dx=cotxcoty (30度,0)2,Obtain the general solution of the differential equationydytan2x/dx=1-y^23,Find the