The bell-shaped curve y = (x) in Figure 16 satisfies dy/dx = xy. Use the Shell Method

The bell-shaped curve y = ƒ(x) in Figure 16 satisfies dy/dx = −xy. Use the Shell Method and the substitution u = ƒ(x) to show that the solid obtained by rotating the region R about the y-axis has volume V = 2π(1 − c), where c = ƒ(a). Observe that as c → 0, the region R becomes infinite but the volume V approaches 2π.

Transcribed Image Text:

C y R a y=f(x) X