5.6 Additional Applications to the Life and Social Sciences

Volume of Solid of Revolution

For function f(x) > 0 on a < x < b and let R be the region under the curve y = f(x) where x = a and x = b. The solid S formed by revolving R about the x axis has volume

Volume of

#10 Find the volume of the solid of revolution formed by rotating the region R about the x axis.

R is the region under the curve from x = -2 to x = 2.

#12 Find the volume of the solid of revolution formed by rotating the region R about the x axis.

R is the region under the curve from x = 1 to x = 10.

#48 VOLUME OF A SPHERE Use integration to show that a sphere of radius r has volume

[Hint: Think of the sphere as the solid formed by rotating the region under the semicircle

Assignment: 5.6 pg. 458 – 7-13 odd, 49