Volumes by Slicing Suppose you have a loaf of bread and you want to ﬁnd the volume of the loaf. One way to do this is to ﬁnd the volume of each slice and then add up their volumes. The volume of a slice of bread is its thickness dx times the area a of the face of the slice (the part you spread butter on). So ΔV ≈ AΔx. In the limit, dV = A(x) dx. (If your loaf of bread is not perfectly regular, the area of a face might change from slice to slice.) To get the entire volume, sum the volumes of all the slices: � V = A(x) dx The Riemann sum approximating this volume looks like n � i=1 has n slices. Ai Δx if the loaf

Volumes by Slicing

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock