Question

Check my work: Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x^2 and y = x about the line x = 5.
v = ∫[0,2] 2πrh dx
r=5-x and h=x-x^2/2

v = ∫[0,2] 2π(5-x)(x-x^2/2) dx = 16π/3

v = ∫[0,2] π(R^2-r^2) dy
R=5-y and r=5-√(2y)
v = ∫[0,2] π((5-y)^2-(5-√(2y))^2) dy = 16π/3

Answer 1

You are correct! Good job! I started this using the washer method and found that it was much more tedious than using the shell method, which worked very well and very easily. Very good work!