By using method of integration,the area of circle x²+y²=a² is
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Given equation of circle is:
x
2
+y
2
=a
2
⇒y
2
=a
2
−x
2
⇒y=
a
2
−x
2
∴ Area of circle =4×Area of first quadrant
=4∫
0
a
ydx
=4∫
0
a
a
2
−x
2
dx
=4[
2
x
a
2
−x
2
+
2
a
2
sin
−1
a
x
]
0
a
=4[0+
2
a
2
sin
−1
a
a
−(0+
2
a
2
sin
−1
a
0
)]
=4[
2
a
2
sin
−1
1−0]
=2a
2
⋅
2
π
=πa
2
square units.
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