Find the area of the region enclosed between the two circles x y and x y 9
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Answered by
2
Step-by-step explanation:
f(x)={cosx:0≤x≤π/4sinx:π/4≤x≤5π/4cosx:5π/4≤x≤2π}
A=∫
0
1
4−(x−2)
2
dx+∫
1
24
4−x
2
dx+
A=[
2
4−(x−2)
2
(x−2)
+
2
4
sin
−1
2
x−2
]
0
1
+[
2
4−(x)
2
(x)
+
2
4
sin
−1
2
x
]
1
2
A=2[(
2
3
(−1)
+2sin
−1
2
−1
)−((−2)(0)+2sin
−1
(−1))+((0)+2sin
−1
(1))−(
2
3
(1)
+2sin
−1
2
1
)]
A=2[
2
−
3
−2sin
−1
(
2
1
)+2sin
−1
(1)+2sin
−1
(1)−
2
3
−2sin
−1
(
2
1
)]
A=2[−
3
−4sin
−1
(
2
1
)+4sin
−1
(1)]
A=2[−
3
−4(π/6)+4(π/2)]
A=2[−
3
+4(π/3)]
A=−2
3
+8(π/3)
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