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Question

Find the area of the region bounded by the ellipse x216+y29=1.

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Solution

The given equation of the ellipse,
x216+y29=1,

the standard form of ellipse is given by
x2a2+y2b2=1

by comparing we get,
a=4 and b=3
It can be observed that the ellipse is symmetrical about x-axis and y-axis.
Area bounded by ellipse =4× Area of OAB
Area of OAB =a0ydx =40ydx

=4031x216dx
=344016x2dx
=34[x216x2+162sin1x4]40

=34[21616+8sin1(1)08sin1(0)]
=34[8π2]
=34[4π]=3π
Therefore, are bounded by the ellipse =4×3π=12π units

395669_425685_ans_df042bb808be4e6f997f9971627ba1fe.png

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