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Find the Volume of a Solid Obtained by the Complete Revolution of the Ellipse X 2 36 + Y 2 25 = 1 About X-axis. - Mathematics and Statistics

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Sum

Find the volume of a solid obtained by the complete revolution of the ellipse `x^2/36 + y^2/25 = 1` about X-axis.

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Solution

From the equation of the ellipse 

`x^2/36 + y^2/25 = 1` 

`y^2 = 25/36 (36 - x^2)`

Lel V be the required volume of the solid obtained by revolving the ellipse about major axis i.e. X-axis. 

V = `pi∫_-6^6 y^2` dx

= `∫_-6^6 25/36(36 - x^2)` dx

= `(25pi)/36 .2 ∫_-6^6 (36 - x^2)` dx ....(by property)

= `(25pi)/18 [36x - x^3/3]_0^6`

= `(25pi)/18 [36(6) - 6^3/3 - 0]`

= `(25pi)/18[144]`

V = 200π cubic units.

Concept: Applications of Definite Integrals
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