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Find the area of the region bounded by t...

Find the area of the region bounded by the ellipse `x^(2)/16+y^(2)/9=1`.

Text Solution

Verified by Experts

The correct Answer is:
`2(sqrt(2)-1)` sq. units

`"Required area "=int_(0)^(pi//2)|sin x-cos x|dx`
`=2int_(0)^(pi//4)(cos x- sin x)dx`
`=2|sin x + cos x|_(0)^(pi//4)`
`=2((1)/(sqrt(2))+(1)/(sqrt(2))-1)=2(sqrt(2)-1)` sq. units.
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