Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 5.

Question

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by  about x = 5.

Quizplus · Accepted Answer

We can use cylindrical shells to revolve the region about x=5. The height of each cylindrical shell will be the difference in the x-coordinates of the two curves, which is (11-x)-(ln(x+1)). The radius of each shell will be the distance from x=5 to the curve closest to it, which is 5-(ln(x+1)). Thus, the volume of each shell will be 2π(5-(ln(x+1)))((11-x)-(ln(x+1))).

The integral to find the volume will be:

V = ∫[0,10] 2π(5-(ln(x+1)))((11-x)-(ln(x+1))) dx

Using a graphing calculator, we can evaluate this integral to be approximately 64.74.

Therefore, the answer is C, 11eaa88b_918f_0121_a696_772cf373e357_TB5869_11, which is the only option closest to 64.74.

Use Cylindrical Shells to Compute the Volume of the Solid