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Mathematics
Problem
The region R is bounded by the circle
x
2
+
y
2
=
4
x^{2}+y^{2}=4
x
2
+
y
2
=
4
and the vertical line
x
=
1
x=1
x
=
1
. Which of the following definite integrals represents the area of R? a)
∫
−
2
2
(
4
−
y
2
−
1
)
d
y
\displaystyle \int_{-2}^{2}\left(\sqrt{4-y^{2}}-1\right)\,dy
∫
−
2
2
(
4
−
y
2
−
1
)
d
y
b)
2
∫
0
3
4
−
y
2
d
y
\displaystyle 2\int_{0}^{\sqrt{3}}\sqrt{4-y^{2}}\,dy
2
∫
0
3
4
−
y
2
d
y
c)
∫
−
3
3
(
4
−
y
2
−
1
)
d
y
\displaystyle \int_{-\sqrt{3}}^{\sqrt{3}}\bigl(\sqrt{4-y^{2}}-1\bigr)\,dy
∫
−
3
3
(
4
−
y
2
−
1
)
d
y
d)
∫
0
3
(
4
−
y
2
−
1
)
d
y
\displaystyle \int_{0}^{\sqrt{3}}\left(\sqrt{4-y^{2}}-1\right)\,dy
∫
0
3
(
4
−
y
2
−
1
)
d
y
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