hw 10 question 10

Question

Find the volume generated by revolving about the x-axis the regions bounded by the following graphs:

x = 1

x = 9

Answer 1

By Disk method volume V = π∫₁⁹(2 + x)dx =π(2x + x²/2)₁⁹ = π[(18 + 81/2) - (2 + 1/2)] = 56π

Answer 2

integrate pir^2 = pi(2+x) = integral of 2pi + pix = 2pix + pix^2/2

evaluate between 1 and 9

18pi + 81pi/2 - 2pi - pi/2 = 56pi = volume