Area of the Region

[Mooch22]

Consider the graph of the function f given by f(x)=(1)/(x+2) for x greater than or equal to 0. Let R be the region bounded by the graph of f, the x- and y-axes, and the vertical line x=k, where k is greater than or equal to 0.

a.) Find the area of R in terms of k.

b.) Find the volume of the solid generated when R is revolved about the x-axis in terms of k.

c.) Let S be the unbounded region in in first quadrant to the right of the vertical line x=k and below the graph of f. Find all values of k such that the volume of the solid generated when S is revolved about the x-axis is equal to the volume of the solid found in part (b).

**Help PLEASE! I'm completely lost!

 

[skeeter]

a. \(\displaystyle R = \int_0^k \frac{1}{x+2} dx\)

b. \(\displaystyle V = \pi \int_0^k \frac{1}{(x+2)^2} dx\)

c. \(\displaystyle \pi \int_0^k \frac{1}{(x+2)^2} dx = \pi \int_k^{\infty} \frac{1}{(x+2)^2} dx\)