Question

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 1 + (y − 6)2, x = 10

Answer 1

i remember these :)

Answer 2

first, you should graph the given curves and find the points of intersection

Answer 3

Here's the graph

Answer 4

I calculated that the intersections are at (10,3) and (10,9)

Answer 5

i wonder if moving it is a good idea ... prolly not at the moment tho

x = 1 + (y − 6)2, x = 10

x-10 = 1 + (y − 6)2, x = 10 - 10

x = 11 + (y − 6)2, x = 0

-x = 11 + (y − 6)2, -x = 0

x = -11 - (y − 6)2, x = 0

Answer 6

Okay, what did you just do there ? lol

Answer 7

i think it's better not to move it...

Answer 8

changing x for y at the moment only orients it normally

y = -11 - (x − 6)^2, y = 0

but yeah ... lets not try to move it this time :)

Answer 9

define the function for height, and radius using the given graph as a guide