Volume -Revolved Around y=2

[kneaiak]

"Find the volume of the solid that is generated when the region in the fourth quadrant bounded by y=-x^2, y=-4, and x=0 is revolved about the line y=2."

I first drew the graph y=-x^2 and y=4 for a visual. My first instinct was to shift y=-x^2 up to the line y=2 as it's the same principal as revolving around the x-axis but I assume that would be incorrect off the bat. The thought was to possibly try the washer method and to use x+2 as the inside radius but that doesn't seem logical. I'm simply stuck from the get go. Any help would be fantastic.

 

[Deleted member 4993]

"Find the volume of the solid that is generated when the region in the fourth quadrant bounded by y=-x^2, y=4, and x=0 is revolved about the line y=2."

I first drew the graph y=-x^2 and y=4 for a visual. My first instinct was to shift -x^2 up to the line y=2 as it's the same principal as revolving around the x-axis but I assume that would be incorrect off the bat. The thought was to possibly try the washer method and to use x+2 as the inside radius but that doesn't seem logical. I'm simply stuck from the get go. Any help would be fantastic.

Did you find the domain and the range of the area to be integrated?

What are those?

 

[kneaiak]

I found the domain to be 0 to 2 but not sure I have the right idea for range, that's where I'm stuck. I think I have the concept of volume around the x-axis and I'd think would be the same principal but it's the y=2 that's tripping me up.