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=?
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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.