Question

Find the volume of the solid generated by revolving the region bounded by x= y^2 -8y +17 and x=2 about the line x=-1

Answer 1

did you try to factor that expression in y

Answer 2

no

Answer 3

but i graphed it. i'm just not sure how to solve it

Answer 4

ok, well you want to
find where it intersects x = 2 and x = -1

Answer 5

we need to solve
y^2 -8y +17 = 2
y^2 -8y +17 = -1 , those will be the points of intersection

Answer 6

y=3, 5, 6, 2

Answer 7

ok wait, lets start over

Answer 8

first we have to graph the region we want to revolve

Answer 9

i'm getting 224pi/15 is that right?

Answer 10

In situations like this, you can simply integrate with respect to y or if you want to make it easier for yourself to think, take the inverse of the function, almost as if you switched the x and y axes. Taking the inverse gives y = x^2 - 8x + 17 and the line it's bounded by becomes y = 2 and you're now revolving it around y = -1.

Answer 11

it helps to graph this region first, or at least get an idea