Volume of the Solid bounds and integral

[alexs2jennisha]

Find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves y= e^{-2x^2}, y=0, x=0, x=1.

Should the bounds for the problem be taken from the y-axis or the x-axis?

I think that the integral for this problem would be:

∏∫(e^{-2x^2})dx , is this correct

 

[haruspex]

∏∫(e^{-2x^2})dx , is this correct

That would be the same as ∏∫ydx, which is clearly wrong.
You need to decide how you want to carve up the volume. You could do it in discs centred on the y axis, but that gets a bit messy because the integral falls into two parts (and it will involve logs). More natural is to carve it into cylinders centred on the y axis.

 

[alexs2jennisha]

Carving it into cylinders still uses the ∏∫R^2dx formula, right? and then my bounds would be on the y axis?

 

[haruspex]

Carving it into cylinders still uses the ∏∫R^2dx formula, right?

Yes, but what is R in this case?

then my bounds would be on the y axis?

No. Each cylinder is centred on the y axis. What are its height, radius and thickness?

 

[alexs2jennisha]

would r be the formula but solved for x?

 

[haruspex]

would r be the formula but solved for x?

I don't know what you mean by that question. r is not much of a formula.
If you take a slice from y = 0 to y = f(x), and from x to x+dx, in the xy plane, then rotate it around the y axis, what do you get? What is its volume? What integral would you write to add up all these volumes between x = 0 and x = 1?