Integral of Bell Curve: Area of Slices

[icystrike]

Can i ask what is the area we are referring to when we take such integral (r is the radius):

$$\int_{-\infty }^{\infty }e^{-r^{2}}dr$$

I'm suspecting that its is the area of slices of bell curve that rotates about the z-axis.

 

[tiny-tim]

hi icystrike!

it's the integral of a vertical slice of the bell curve through its centre

 

[HallsofIvy]

You understand, I hope, that finding area is one possible application of the integral. When we calculate an integral we are not necessarily finding any area at all!

 

[icystrike]

Thanks tiny-tim and HallsofIvy!

Yes! I know that! We can use Integral to compute things like work, flux, centroids .. =D

Its just that my teacher actually relate the slice as "some slice that is parallel to the y-axis" while i think that it should be the slice that is passing through origin(He've probably made some mistake)... (My teacher was actually comparing the volume of a rotated bell curve about z axis by slice and shells to evaluate the area under bell curve - $$A^{2}=\pi$$ )

 

[tiny-tim]

hi icystrike!

Its just that my teacher actually relate the slice as "some slice that is parallel to the y-axis" while i think that it should be the slice that is passing through origin

i think he means that it'll be the same (it's the same shape), apart from a factor e^-x2

 

[icystrike]

Oh! Thats what he meant! Truly enlighten! Thanks Tim! :)
(Came to ensure that i get the concept right)