Question

Why is that when i am trying to use the shell method for this problem: y=5x+6 and y=x^2, rotated about the x axis, i have to break it up into two integrals.

Answer 1

well, lets draw it :)

Answer 2

since you have a odd spot that you have to account for, its best to do it in parts

Answer 3

ah, i see that small portion below y=1

Answer 4

the equations for the area change at that point :)

Answer 5

so the radius of that would still be y

Answer 6

correct, the radius of the shell doesnt change; just the equations that define the area

Answer 7

but what would be the heigh, woudl it just be sqrtx-0

Answer 8

lets turn this to see it in a normal view point