Hi there!
Looks like a lot of work is going on here.
Let's start by solving this equation for the x.
Step 1) Add -20y to both sides.
Step 2) Divide both sides by 5.
Final Answer:
Now, let's solve for y.
Step 1) Add -5x to both sides.
Step 2) Divide both sides by 20.
Final Answer:
Hope this helps! :D
Hint - When you have two variables in an equation, and you want to solve for one, the other will end up in your answer. :)
The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.
Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is
π (radius) (height) = π (1/y)² ∆y = π/y² ∆y
and the volume of a stack of n such disks is
where is a point sampled from the interval [1, 5].
As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,
