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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Answers
Answered by
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
Answered by
9
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
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