Answer:
Step-by-step explanation:
To solve the equation, isolate x. Whatever you do to isolate x one on side, you must do to the other.
1) Multiply both sides by 9 to get rid of the fractions.
2) Distribute the 3 to 8x and 15. Then, combine like terms.
3) Move the 66 to the other side, subtracting 18 by 66, then divide each side by 20 to finally isolate x.
Thus, .
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,
