# Calculus,Sketch a washer and Find the Volume of the Solid generatedBy Revolving the region bounded by y=2x^2, y=0, and x=2 around the y-axis?

• Shell method:

height = 2x^2

Volume = 2 pi ∫ x (2x^2) dx , x=0 to 2

= 4 pi ∫ x^3 dx , x=0 to 2

= 16 pi

Washer:

Volume = pi ∫ (2^2 – (sqrt(y/2))^2 ) dy, y=0 to 8

= pi ∫ (2^2 – y/2 ) dy, y=0 to 8

= 16pi

Hottest videos
Related Posts