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Find area enclosed by ellipse (x^(2))/(1...

Find area enclosed by ellipse `(x^(2))/(16) + (y^(2))/(9) = 1`

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Given curve is an ellipse which is symmetric about X-axis and both, as shown in the figure.

` :. ` Area bounded by ellipse
`=4xx` (area of shaded region in first quadrant)
`=4 xx int_(0)^(2)ydx=4 int_(0)^(2)(3)/(2)sqrt(4-x^(2))dx`
`=6int_(0)^(2)sqrt(2^(2)-x^(2))dx`
`=6[(x)/(2)sqrt(4-x^(2))+(2^(2))/(2)"sin"^(-1)((x)/(2))]_(0)^(2)`
`=6{0+2"sin"^(-1)(1)-0}`
`=6xx2xx((pi)/(2))`
`=6pi` sq. units.
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