Let R be the region bounded by . Compute the volume of the solid formed by revolving R about x = 2.

Question

Let R be the region bounded by  . Compute the volume of the solid formed by revolving R about x = 2.

Quizplus · Accepted Answer

We can use the disk method to calculate the volume of the solid formed by revolving R about x = 2. For any value of x, the distance between x and the line x = 2 is 2 - x. The radius of the disk at x is given by the function f(x) = sqrt(x + 1). The area of the disk at x is then given by pi*(f(x))^2. Thus, the volume of the solid is given by the integral:

V = ∫[1,3] pi*(2-x)*(sqrt(x+1))^2 dx

This integral can be simplified using algebra and evaluated using substitution or integration by parts. The result is:

V = pi*(68/15)

Which is approximately equal to 14.25. Therefore, the correct answer is choice C.

Let R Be the Region Bounded by