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

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

A

`10pi`

B

`11pi`

C

`12pi`

D

`13pi`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^2/16+y^2/9=1`
`y^2/9=(16-x^2)/16`
`y^2=9/16(16-x^2)`
`y=pm3/4sqrt(16-x^2)`
I=`4int_0^4 ydx`
=`4int_0^4sqrt(16-x^2)`
=`3(1/2xsqrt(16-x^2)+16/2sin^(-1)x/4)_0^4`
=`3(4/2sqrt(16-16)+16/2sin^(-1)(4/4)-0-0)`
...
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