Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^5, y=1 and the y-axis and whose cross -sections perpendicular to the y-axis are equilateral triangles.
I don't know what the bounds for the integral would be when I try to calculate the volume. I put everything in terms of x and so I got the volume to be
V=1/8(40/7x^(7/5)-5/4x^(8/5)),
which then needs to be evaluated by the bounds. I am not sure if my process is right and help would be appreciated.
each triangle has a base of length x, making its area √3/4 x^2
since x = y^(1/5) we have
v = ∫[0,1] √3/4 y^(2/5) dy = √3/4 * 5/7 y^(7/5) [0,1] = 5√3/28
okay thank you so much for the help!
i just tried to hand this in on my homework site and it said it was incorrect
also I got that each triangle would have a sidelength of x=5root(y) because I was told to set it in terms of y.
how about writing that as (5/7) sqrt (3/4)
or maybe sqrt (25/196