Question

Evaluate the area bounded by the ellipse `(x^2)/(4)+(y^2)/(9)=1` above the x-axis.

Answer 1

The given ellispse meets the x-axis at A (-2,0) and B (2,0)
`(x^2)/(4)+(y^2)/(9)=1 y= 3/2 . sqrt(4-x^2)`
`therefore` required area `=underset(-2)overset(2)inty dx=3/2.underset(-2)overset(2)intsqrt(4-x^2)dx`
`= 2xx 3/2 xx underset(0)overset(2)intsqrt(4-x^2)dx`
`=6.underset(0)overset(pi//2)intcos^2 thetad theta` where x=2 sin `theta`