find the area of the smaller region bounded by the ellipse x square divided by 9 + y square divided by 4 which is equal to 1. and the line x divided by a + y divided by b which is equal to 1
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Answer:
Area BCAB=Area (OBCAO)−Area (OBAO)
=∫
0
3
2
1−
9
x
2
dx−∫
0
3
2(1−
3
x
)dx
=
3
2
[∫
0
3
9−x
2
dx]−
3
2
∫
0
3
(3−x)dx
=
3
2
[
2
x
9−x
2
+
2
9
sin
−1
3
x
]
0
3
−
3
2
[3x−
2
x
2
]
0
3
=
3
2
[
2
9
(
2
π
)]−
3
2
[9−
2
9
]
=
3
2
[
4
9π
−
2
9
]
=
3
2
×
4
9
(π−2)
=
2
3
(π−2) sq. units
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