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,


Answer:
a. Probability = 0.15
b. Probability = 0.3
Step-by-step explanation:
Given




Solving (a): Probability of being somewhere else
This is calculated by subtracting the sum of given probabilities from 1.



Solving (b): Probability of being in bedroom or kitchen
This is calculated as:



Answer:
Step-by-step explanation:
61% = 0.61
0.68
2/3 = 0.666
0.57
3/5 = 0.600
least to greatest : 0.57, 3/5, 61%, 2/3, 0.68