Asked by Anonymous
Find the volumes of the solids generated by revovling the region in the first quadrant bounded by the curve x=4y-4y^3 and the y-axis about the given axes:
a. the x-axis
b. the line y=1
NO idea how to set it up!!! HElP!!
a. the x-axis
b. the line y=1
NO idea how to set it up!!! HElP!!
Answers
Answered by
Steve
the function is
x = 4y(1-y^2)
so you know it crosses the y-axis at -1,0,1
So you're dealing with the bump in QI from y=0 to 1
To revolve that about the x-axis, I'd suggest shells, so
v = integral[0,1] 2pi r*h dy
where r = y, and h = x
v = 2pi integral[0,1] y(4y-y^3) dy
= 2pi Integral 4y^2 - y^4 dy
= 2pi (4/3 y^3 - 1/5 y^5) [0,1]
= 2pi (4/3 - 1/5)
= 34pi/5
Around y=1, same formula, but now r = 1-y.
x = 4y(1-y^2)
so you know it crosses the y-axis at -1,0,1
So you're dealing with the bump in QI from y=0 to 1
To revolve that about the x-axis, I'd suggest shells, so
v = integral[0,1] 2pi r*h dy
where r = y, and h = x
v = 2pi integral[0,1] y(4y-y^3) dy
= 2pi Integral 4y^2 - y^4 dy
= 2pi (4/3 y^3 - 1/5 y^5) [0,1]
= 2pi (4/3 - 1/5)
= 34pi/5
Around y=1, same formula, but now r = 1-y.
Answered by
Anonymous
I did that already and got it incorrect
Answered by
Anonymous
nevermind i see what i did wrong