Let R be the region bound by the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on theinterval 0 ≤ x < π. b) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis.

c) Write, but do not solve, an equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x = –1.

b.

(c)

Step-by-step explanation:

b. The volume of solid formed is given by the washers formula as follows;

Therefore, we have, the integral expression whose solution is the volume formed by rotating 'R', about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is given as follows;

(c)  We have;

x = arcos(y - 2), x = arcsin(1/y)

At x = 0, y = 2 + cos(0) = 3

csc(0) = ∞

At x = π, y = 2 + cos(π) = 2 + -1 = 1

csc(π) = ∞

Therefore, we get;

-18 degrees is the answer : )