Question

Q. Calculate the area of the region enclosed between the circles: x2 + y2 = 16 and (x + 4)2 + y2 = 16.
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Sραɱɱҽɾ ʂƚαყ αɯαყ..
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Answer 1

Here x

2

+y

2

=16

∴y

2

=16−x

2

y=

4

2

−x

2

Area =

0

∫

π/2

4 2 −x 2 dx

=[ 2]

x( 4 2 −x 2 ) + 24 2

sin −1 ( 4π )] 0π/2

=( 24(0) + 216 sin −1 (1))−(0+ 216 sin −1 (0))

=0+8( 2π )−0

∴ Required area =4π

Answer 2

Answer:

Here x

2

+y

2

=16

∴y

2

=16−x

2

y=

4

2

−x

2

Area =

0

∫

π/2

4

2

−x

2

dx

=[

2

x(

4

2

−x

2

)

+

2

4

2

sin

−1

(

4

π

)]

0

π/2

=(

2

4(0)

+

2

16

sin

−1

(1))−(0+

2

16

sin

−1

(0))

=0+8(

2

π

)−0

∴ Required area =4π