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;

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation:

step-by-step explanation:

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