Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. x2 9y2

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Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.

x² + 9y² = 9

(a) About

y = 3

(b) About  

x = 3

a) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

b) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

Step-by-step explanation:

a) the volume of solid of revolution

about y=3

Using SHELL METHOD;

Volume V = 2π . (3-y) (2.3√(1-y²)) dy

= 12π .  (3-y) √(1-y²) dy

= 12π .  (( 3√(1-y²) - y(√(1-y²)) dy

= 12π[ π - 0 ]

= 18π² = 177.652879 ≈ 177.65288

Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

b)

the volume of solid of revolution

about x=3

Using SHELL METHOD;

Volume V = π . (3-x) (√(9-x²)) dx

= π . (3-x) √(9-x²) dx

= π . (3√9-x² -x√(9-x²) dx

=  π [ - 0 ]

= 18π² = 177.652879 ≈ 177.65288

Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288

the answer is 99.

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