Need help with this

[Hunter_0132451]

I am trying to find the volume of the equation when it is rotated by the x axis and this is what i got but i need to confirm if i am on the right path because i am questioning if this is right. the original equation was bound by the curve y=e^-x and both the x and y axis only in the first quadrant. the area was one apologies for the horrible handwriting

 

[Dr.Peterson]

I am trying to find the volume of the equation when it is rotated by the x axis and this is what i got but i need to confirm if i am on the right path because i am questioning if this is right. the original equation was bound by the curve y=e^-x and both the x and y axis only in the first quadrant. the area was one apologies for the horrible handwriting

Looks good to me. You don't really have to take a limit at 0, but that doesn't hurt.

Why aren't you confident?

 

[Hunter_0132451]

Looks good to me. You don't really have to take a limit at 0, but that doesn't hurt.

Why aren't you confident?

mainly because I am worried about the nitty gritty stuff which can screw me over and now i have to do this thing again with both the shell method and disc method as well